Square root of complex number on a calculator

[Gremlin]

I'm working through some examples in a textbook but i am unable to get the desired answer on my calculator, i keep getting math error and various other results which are not the answer I'm looking for.

What i have is:

√ 62.9∠88.2 / 0.00165∠72.3

Please could someone tell me what answer you get and i'll see if it matches what i have in my textbook. If it does i'd be interested to know exactly how you entered it into the calculator.

If the above isn't clear it's the sq root of 62.9∠88.2 / 0.00165∠72.3.

Thanks.

 

[Svein]

Please could someone tell me what answer you get and i'll see if it matches what i have in my textbook. If it does i'd be interested to know exactly how you entered it into the calculator.

The nominator should be the square root of 62.9 at an angle of half of 88.2°. Now divide the magnitudes and subtract the angles.

 

[Jeff Rosenbury]

It is still not clear.

If I remember my orders of precedence you mean sqrt(62.9on the angle 88.2) all ÷0.00165on the angle72.3.

Since the square root is set of functions on a number which when the result is squared return the number, what resultant numbers will do that?

Do you know how to multiply and divide in phasor notation?

 

[Gremlin]

The nominator should be the square root of 62.9 at an angle of half of 88.2°. Now divide the magnitudes and subtract the angles.

I want to take the sq root of 62.9∠88.2 / 0.00165∠72.3

When i do that division on the calculator in isolation i get 38121.2∠15.9

Now if on the calculator (Casio fx-3650P) i do: √38121.2∠15.9 i get 195.2∠15.9

The answer my textbook says i should get is 195∠8

 

[Jeff Rosenbury]

The nominator should be the square root of 62.9 at an angle of half of 88.2°. Now divide the magnitudes and subtract the angles.

That is the most popular answer. It is like saying the square root of 4 is 2. Yet -2 is also an sometimes answer depending on how the question is phrased. There are other phase angles which when doubled add up to 88.2. Which are valid answers depend on the original problem. If the original question is, what is the square root of X, you are of course correct.

But if the original question results from some physical system other, potentially nonsensical, answers may occur.

 

[momoko]

You need to halve the argument so your textbook's answer looks right.

 

[Gremlin]

You need to halve the argument so your textbook's answer looks right.

I did't know that. Is there a way of inputting it into the calculator so the calculator gets it right?

 

[Svein]

Now I see a problem. Is the square root over the complete expression or just over the nominator?

 

[vela]

I want to take the sq root of 62.9∠88.2 / 0.00165∠72.3

When i do that division on the calculator in isolation i get 38121.2∠15.9

Now if on the calculator (Casio fx-3650P) i do: √38121.2∠15.9 i get 195.2∠15.9

The answer my textbook says i should get is 195∠8

Your problem is similar to how you're writing. The question people have been asking you is whether you're trying to calculate
$$\sqrt{\frac{62.9 e^{i88.2^\circ}}{0.00165 e^{i72.3^\circ}}}$$ or
$$\frac{\sqrt{62.9 e^{i88.2^\circ}}}{0.00165 e^{i72.3^\circ}}.$$ If you simply used parentheses, it would have cleared up the ambiguity, i.e., √ (62.9∠88.2 / 0.00165∠72.3). Therein lies the root of your problem. Use parentheses as appropriate on your calculator as well.

 

[Gremlin]

√ (62.9∠88.2 / 0.00165∠72.3). Therein lies the root of your problem. Use parentheses as appropriate on your calculator as well.

When i input it into the calculator exactly as you have it above i get "math error".

 

[SammyS]

When i input it into the calculator exactly as you have it above i get "math error".

How about trying
√ ((62.9∠88.2) / (0.00165∠72.3))

 

[Mark44]

That is the most popular answer. It is like saying the square root of 4 is 2.

The square root of 4 is 2. Period.

Yet -2 is also an sometimes answer depending on how the question is phrased.

Not if the question is, "what is the square root of 4?" The expression $\sqrt{4}$ has only one value, +2. It is true that 4 has two square roots, but by definition and long usage, the symbol $\sqrt{x}$ means the positive square root of x. I am assuming here the real-valued function, where x $\ge$ 0.

There are other phase angles which when doubled add up to 88.2. Which are valid answers depend on the original problem. If the original question is, what is the square root of X, you are of course correct.

But if the original question results from some physical system other, potentially nonsensical, answers may occur.

 

[Jeff Rosenbury]

The square root of 4 is 2. Period.
Not if the question is, "what is the square root of 4?" The expression $\sqrt{4}$ has only one value, +2. It is true that 4 has two square roots, but by definition and long usage, the symbol $\sqrt{x}$ means the positive square root of x.

Did I claim differently?

I claimed that if the question is phrased differently, the other root needs to be considered. Since the OP clearly wasn't presenting the problem in the way it was originally phrased, I thought this point should be mentioned.

 

[Mark44]

Did I claim differently?

Yes. Here is what you said, verbatim:

That is the most popular answer. It is like saying the square root of 4 is 2. Yet -2 is also an sometimes answer depending on how the question is phrased.

-2 is never the answer if the question is, "what is the square root of 4?"

However, if the question is, "what are the two numbers whose square is 4?", then I agree that the two numbers are 2 and -2. If we're talking about the square root of a number, we're talking about the principal, or positive square root.

I claimed that if the question is phrased differently, the other root needs to be considered. Since the OP clearly wasn't presenting the problem in the way it was originally phrased, I thought this point should be mentioned.

 

[Gremlin]

How about trying
√ ((62.9∠88.2) / (0.00165∠72.3))

Math error.

 

[Svein]

Your calculator cannot deal with this notation. Do it this way:

1. Divide 62.9 by 0.00165 (= 38 121.21212)
2. Subtract 72.3 from 88.2 (= 15.9)
3. Take the square root of the result in 1 (= 195.246). That is the magnitude of the answer.
   
4. Divide the result in 3. by two (= 7.95). That is the angle of the answer.

There you are.

 

[Gremlin]

Your calculator cannot deal with this notation. Do it this way:

1. Divide 62.9 by 0.00165 (= 38 121.21212)
2. Subtract 72.3 from 88.2 (= 15.9)
3. Take the square root of the result in 1 (= 195.246). That is the magnitude of the answer.
   
4. Divide the result in 3. by two (= 7.95). That is the angle of the answer.

There you are.

So if you don't know to sq root the result of dividing the magnitudes and then half the result of subtracting the angles (which i didn't or had forgotten), you'd be knackered basically.

Thanks for clearing that up.

 

[Jeff Rosenbury]

So what you are saying is: "What is the square root of 4?" brings an answer of 2 (i.e. the most popular answer; other unpopular answers being wrong.) But if phrased as "What are two numbers whose square is 4?", then 2 and -2 are both correct?

More particularly if phrased as "In a 60 Hz system, what voltages (across a purely resistive load) would give a power 195 on an angle 8º?" Then, other answers might matter.

A deeper understanding of the math than simply knowing how to push buttons on the calculator is essential to good engineering. I would think it helps in science as well.

 

[Svein]

A deeper understanding of the math than simply knowing how to push buttons on the calculator is essential to good engineering. I would think it helps in science as well.

Oh, I agree completely. But introducing mathematical rigor on a too early stage is likely to confuse.
I could, of course have added: "15.9° under the root sign is also equal to 360° + 15.9°, therefore halving the angle gives two answers; 7.95° and 187.95°". But, as his textbook states that the answer is 8°, I let well enough alone.

 

[vela]

So if you don't know to sq root the result of dividing the magnitudes and then half the result of subtracting the angles (which i didn't or had forgotten), you'd be knackered basically.

Generally speaking, it's not a good idea to rely on a calculator to find answers you don't know how, in principle, to get by hand.

 

[vela]

So what you are saying is: "What is the square root of 4?" brings an answer of 2 (i.e. the most popular answer; other unpopular answers being wrong.) But if phrased as "What are two numbers whose square is 4?", then 2 and -2 are both correct?

The phrase "the square root of 4" refers, by convention, to the principal square root of 4, denoted by $\sqrt 4$, which, by definition, is always +2 and never -2. Is -2 a square root of 4? Sure, but it's not an answer to the question, "What is the square root of 4?"

More particularly if phrased as "In a 60 Hz system, what voltages (across a purely resistive load) would give a power 195 on an angle 8º?" Then, other answers might matter.

But this is a completely different question (and an ill-posed one as there are no units on the number 195). No one is arguing that if you want to solve the equation $x^2=4$ that you need to include the second root to be complete, but that's different than saying $x = \sqrt{4}$.

A deeper understanding of the math than simply knowing how to push buttons on the calculator is essential to good engineering. I would think it helps in science as well.

Of course it is, and no one is saying it isn't. At the same time, it's important that one can communicate clearly and follow standard conventions. You don't write, for example, the quadratic equation as
$$x = \frac{-b + \sqrt{b^2-4ac}}{2a}$$ and then claim that everyone should know there are two square roots so using the plus/minus symbol is unnecessary or incorrect.

 

[Ray Vickson]

The square root of 4 is 2. Period.
Not if the question is, "what is the square root of 4?" The expression $\sqrt{4}$ has only one value, +2. It is true that 4 has two square roots, but by definition and long usage, the symbol $\sqrt{x}$ means the positive square root of x. I am assuming here the real-valued function, where x $\ge$ 0.

I must disagree: many descriptions distinguish between "square root of $x$" and the "sqrt(x)" or "$\sqrt{x}$ or "$x^{1/2}$" function. According to http://en.wikipedia.org/wiki/Square_root : "In mathematics, a square root of a number a is a number y such that y^2 = a, in other words, a number y whose square (the result of multiplying the number by itself, or y × y) is a.[1] For example, 4 and −4 are square roots of 16 because 42 = (−4)2 = 16." It goes on to say further: "Although the principal square root of a positive number is only one of its two square roots, the designation "the square root" is often used to refer to the principal square root. For positive a, the principal square root can also be written in exponent notation, as a^(1/2)." My understanding of the terms has for decades been in line with the Wikipedia explanation.

 

[Mark44]

Ray, my remarks refer primarily to what Jeff Rosenbury said. I took what he said as implying that for $\sqrt{4}$, 2 was the "most popular" answer, but that there was another answer, -2. vela seems to be saying pretty much the same as what I said.

 

[Ray Vickson]

Ray, my remarks refer primarily to what Jeff Rosenbury said. I took what he said as implying that for $\sqrt{4}$, 2 was the "most popular" answer, but that there was another answer, -2. vela seems to be saying pretty much the same as what I said.

I agree: he said "the" square root, rather than "a" square root (but he did not use the symbol $\sqrt{4}$).

 

[Jeff Rosenbury]

I met a grad student when I was in school. He told me a story of how, when a general at his job had said something really stupid, he insisted the general was wrong. Thus instead of being an employed engineer he was in grad school after being fired when the general canceled his project rather than be embarrassed.

Since then I've been more open to other people's opinions even when I think they are stupid. I've learned to ask what people mean instead of simply assuming they are idiots. I use less precise language at the beginning of conversations to help us as a group to arrive at the right answer rather than degenerate into acrimony. Sometimes it even happens that they are right and I'm wrong.

Thus I tend to choose words like "unpopular" instead of "what kind of idiot would think that?"

The goal is to reach the truth, not score points by "proving" the other guy is wrong.

I have not disagreed with your points. So why is this discussion still going on?

 

[Mark44]

I met a grad student when I was in school. He told me a story of how, when a general at his job had said something really stupid, he insisted the general was wrong. Thus instead of being an employed engineer he was in grad school after being fired when the general canceled his project rather than be embarrassed.

Since then I've been more open to other people's opinions even when I think they are stupid. I've learned to ask what people mean instead of simply assuming they are idiots. I use less precise language at the beginning of conversations to help us as a group to arrive at the right answer rather than degenerate into acrimony. Sometimes it even happens that they are right and I'm wrong.

Thus I tend to choose words like "unpopular" instead of "what kind of idiot would think that?"

The goal is to reach the truth, not score points by "proving" the other guy is wrong.

I have not disagreed with your points. So why is this discussion still going on?

Because at this forum we have seen people write stuff like this many, many times:

$\sqrt{4} = \pm 2$

Using less precise language at the start of a conversation might seem more tactful, but IMO it leads to misunderstanding rather than clarity. No one here is out to prove you wrong, but we do our best to rectify statements that are incorrect.

 

[Jeff Rosenbury]

Using less precise language at the start of a conversation might seem more tactful, but IMO it leads to misunderstanding rather than clarity. No one here is out to prove you wrong, but we do our best to rectify statements that are incorrect.

So the proper response to a mistake on the homework forum is to be rude and cut off communication.

Hmm.

I prefer a community which responds to mistakes by seeking truth together. But I'm only one guy, so perhaps you are right.

 

[Jeff Rosenbury]

Ray, my remarks refer primarily to what Jeff Rosenbury said. I took what he said as implying that for $\sqrt{4}$, 2 was the "most popular" answer, but that there was another answer, -2. vela seems to be saying pretty much the same as what I said.

Had I meant "But" I would have written "But". I used the word "Yet" which has the connotation of agreeing with the previous statement.

"But" - Conjunction used to express difference.

"Yet" - Conjunction used to express added material.

So perhaps my mistake is in using English rather than whatever is taught in school these days.

 

[Mark44]

So the proper response to a mistake on the homework forum is to be rude and cut off communication.

That's not at all what I said. How were my remarks rude or cut off communication?

Hmm.

I prefer a community which responds to mistakes by seeking truth together. But I'm only one guy, so perhaps you are right.