# Square root of complex number on a calculator

1. Jun 6, 2015

### Gremlin

I'm working through some examples in a text book 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 text book. If it does i'd be interested to know exactly how you entered it into the calculator.

If the above isnt clear it's the sq root of 62.9∠88.2 / 0.00165∠72.3.

Thanks.

2. Jun 6, 2015

### Svein

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.

3. Jun 6, 2015

### 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?

4. Jun 6, 2015

### Gremlin

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 text book says i should get is 195∠8

5. Jun 6, 2015

### Jeff Rosenbury

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.

6. Jun 6, 2015

### momoko

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

7. Jun 6, 2015

### Gremlin

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

8. Jun 6, 2015

### Svein

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

9. Jun 6, 2015

### vela

Staff Emeritus
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.

10. Jun 6, 2015

### Gremlin

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

11. Jun 6, 2015

### SammyS

Staff Emeritus
√ ((62.9∠88.2) / (0.00165∠72.3))

12. Jun 6, 2015

### Staff: Mentor

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.

13. Jun 6, 2015

### Jeff Rosenbury

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.

14. Jun 7, 2015

### Staff: Mentor

Yes. Here is what you said, verbatim:
-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.

15. Jun 7, 2015

### Gremlin

Math error.

16. Jun 7, 2015

### 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.

17. Jun 7, 2015

### Gremlin

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.

18. Jun 7, 2015

### 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.

19. Jun 7, 2015

### Svein

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.

20. Jun 7, 2015

### vela

Staff Emeritus
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.