# Using complex numbers to solve for a current in this circuit

GJ1
Homework Statement:
I am having trouble solving this equation, it is for an physics/electronics course
Relevant Equations:
[50/(4+j3)(50)+100]x150
First I solved 4+j3, which I squared 4 and 3 to equal 16 and 9 then I added them to get 25 and then I got the square root of 25 = 5.

Then I plugged it back in to the equation.
[50/(5)(50)+100] x 150 to get 50/350x 150= 1/7(150)= 21.42. I've attached the correct answer.

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Homework Statement:: I am having trouble solving this equation, it is for an physics/electronics course
Relevant Equations:: [50/(4+j3)(50)+100]x150
That doesn't look like an unambiguous mathematical expression.
First I solved 4+j3, which I squared 4 and 3 to equal 16 and 9 then I added them to get 25 and then I got the square root of 25 = 5.
Well, okay. That's the magnitude of that complex number.
Then I plugged it back in to the equation.
[50/(5)(50)+100] x 150 to get 50/350x 150= 1/7(150)= 21.42. I've attached the correct answer.
I can't make any sense of what you've attached. What are you actually trying to do here?

MatinSAR
GJ1
The equation is for current in a circuit, it's in the picture that I've attached. It includes a complex number for the reactive properties in the current "4+3i" or 4+3j. When, I sive the equation for I1, I get 21.42, the actual number is 20 - 10j or 20-10i.

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The equation is for current in a circuit, it's in the picture that I've attached. It includes a complex number for the reactive properties in the current "4+3i" or 4+3j. When, I sive the equation for I1, I get 21.42, the actual number is 20 - 10j or 20-10i.
Okay, so the answer is a complex number, but you somehow got rid of the imaginary part and replaced the complex number ##4 + 3j## with ##5##?

GJ1
But, how is the answer 20-10j

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But, how is the answer 20-10j
First I solved 4+j3, which I squared 4 and 3 to equal 16 and 9 then I added them to get 25 and then I got the square root of 25 = 5.
Does that mean that you got ##4 + j3 = 5##?

Note that ##|4 + j3| = 5##.

GJ1
Yes

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Yes
You're obviously misunderstanding something fundamental about complex numbers. ##4 +j3 \ne 5##

GJ1
How would I add this complex number in this equation

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How would I add this complex number in this equation
It's difficult to help you, because the expression you wrote in the original post is unclear. Although, I think I can see from your calculations what you mean.

Basically, the answer is a complex number. It's a simplification of the complex number you started with. The key is to express ##\dfrac 1 {4 +j3}## as a complex number in standard (Cartesian) form.

The standard method for doing this is to use the complex conjugate:
$$\dfrac 1 {4 +j3} = \dfrac {4 - j3}{(4+j3)(4-j3)} = \dots$$Does any of that look familiar?

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1) Make sure that you make your formulas unambiguous. Use parentheses; they are cheap.
Is that 50/( (4+j3)(50) )or ( 50/(4+j3) )(50)?
2) Often the first step in manipulating a fraction with a complex denominator ##1/(a+bj)## is to multiply both the numerator and denominator by the complex conjugate of the denominator to get ##(a-bj)/(a^2+b^2)##.

scottdave and GJ1
GJ1
I have limited experience with complex numbers, this is the first that I've had to use them. If I see how this equation is solved, it will go along way in my understanding of them.

PeroK
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I have limited experience with complex numbers, this is the first that I've had to use them. If I see how this equation is solved, it will go along way in my understanding of them.
I doubt that!

Technically, we can't do your homework for you, and we expect you to have the required skills for the courses you are taking. You need to revise (or learn) Complex Numbers asap.

GJ1
1) Make sure that you make your formulas unambiguous. Use parentheses; they are cheap.
Is that 50/( (4+j3)(50) )or ( 50/(4+j3) )(50)?
2) Often the first step in manipulating a fraction with a complex denominator ##1/(a+bj)## is to multiply both the numerator and denominator by the complex conjugate of the denominator to get ##(a-bj)/(a^2+b^2)##.
It's (50/(4+j3)(50)

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It's (50/(4+j3)(50)
Which is simply ##\frac 1 {4 +j3}##.

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It's (50/(4+j3)(50)
Although, what I think it should be is:
$$\frac{50}{(4 + j3)(50) + 100}$$

FactChecker
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Complex numbers have all the properties of real numbers and more.
## (50/(4+3j))*50 = 1/(4+3j) = \frac {4-3j}{(4+3j)(4-3j)} = \frac {4-3j}{4^2+3^2} = \frac {4}{25} - \frac {3}{25}j##

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Although, what I think it should be is:
$$\frac{50}{(4 + j3)(50) + 100}$$
The OP must make clear how much is in the numerator and in the denominator using carefully placed parenthesis.

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It's (50/(4+j3)(50)
That clarifies nothing. Is that final (50) in the numerator or in the denominator? Also, placing '()' around that final 50 doesn't help anything.

GJ1
I doubt that!

Technically, we can't do your homework for you, and we expect you to have the required skills for the courses you are taking. You need to revise (or learn) Complex Numbers as see

This is invalid. Please be more careful with your parenthesis. Where is the ')' that matches the first '('?
[50/(4+j3)(50)+100]x150 This is the equation

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[50/(4+j3)(50)+100]x150 This is the equation
I would normally interpret that as ##[\frac {50(50)}{(4+j3)} + 100 ]150##. Is that right?

GJ1
50 divided by (4+j3) x 50 +100

GJ1
The denominator is(4+j3)x50+100

GJ1
The answer that was given is 20-j10

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$$\bigg [\frac{50}{(4 + j3)(50) + 100} \bigg ] \times 150 = 20 -j10$$

GJ1
Yes, That is how the equation is given.

Mentor
It's (50/(4+j3)(50)
As already noted, this is ambiguous. Also, the parentheses aren't matched -- there are three left parens and two right parens.
Which is simply 14+j3.
Assuming that the ambiguous expression above is ##\frac {50}{(4 + j3)50}##. As written, it could be interpreted as ##\frac{50}{4 + j3}\cdot 50## or ##\frac{2500}{4 + j3}##.
[50/(4+j3)(50)+100]x150 This is the equation
That is not an equation. An equation always has an = symbol somewhere in the middle.

 50/[(4+3j)x50+100]x150=20-10j

GJ1
 50/[(4+3j)x50+100]x150=20-10j
How did the get 20-10j as the answer

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For homework, we should only give hints and guidance. Use the fact that ##\frac {1}{a+bj} = \frac {a-bj}{(a+bj)(a-bj)} = \frac {a-bj}{a^2+b^2} = \frac {a}{a^2+b^2} - \frac {b}{a^2-b^2} j## and see what you get.

GJ1
This was not a homework assignment, it's not necessary to understand the equation for this course, I was just interested in how they derived their answer.

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This was not a homework assignment, it's not necessary to understand the equation for this course, I was just interested in how they derived their answer.
I should have said that we are only supposed to give hints and directions in a homework type of question. I think you should give it another try using the hint in my post #30 above.

Mentor
50/[(4+3j)x50+100]x150=20-10j
Although you have parentheses and brackets in your work, you don't have enough of them.

50/[(4+3j)x50+100]x150 means this:
$$\frac{50}{(4 + 3j) \cdot 50 + 100} \cdot 150$$
The above equals $$\frac {7500}{(4 + 3j) \cdot 50 + 100}$$
and does not equal 20 - 10j.

$$\frac{50}{(4 + 3j) \cdot 50 + 100} \cdot 150$$
The above equals $$\frac {7500}{(4 + 3j) \cdot 50 + 100}$$
$$\bigg [\frac{50}{(4 + j3)(50) + 100} \bigg ] \times 150 = \frac{150}{(4 + j3) + 2}= \frac{50}{2+ j} = \frac{(50)(2 - j)}{5} = 20 - j10$$