# How to solve two equations involving complex variables?

• shaiqbashir
In summary: You can solve equations involving complex variables by separating the real and imaginary parts on the left and right hand side of the equation.
shaiqbashir
how to solve two equations involving complex variables??

Hi guys!

well! i want to know how can u solve the following two equations simultaenously in order to find out Ix and Iy:

(3+j4)Ix - j4Iy=10-------------(1)
(2-j4)Ix +j2Iy=0---------------(2)

please tell me the best methods to solve these two equations. How can i solve them with my scientific calculator?

Please tell me both ways:

solving manually

and solving through scientific calculator.

I shall be thankful to u for this act of kindness.

Take carez!

Good Bye!

What do "j4" and "J2" mean? I assume j is your engineer's way of writing the imaginary unit that I would call i, but what are the 4 and 2 after them. If they are intended to mean powers, i^4 and i^2, then i2= -1 and i4= 1, of course.

HEy it's the way we write in circuits. I am looking for the same thing, how do you solve equations involving complex numbers by hand? My calculator doesn't do it.

So according to his equation, it means:

(3+4i) Ix - 4i Iy=10-------------(1)
(2-4i) Ix +2i Iy=0---------------(2)

And it's not a square of i. Please explain. Thanks.

We use j instead of i in circuits. And 3i is written as j3. It means the same.

@sonutulsiani,
And what about that big 'I'? What is meant by Ix, Iy etc?

Ix and Iy are currents. Do you know how to solve?

You posed your question as if the fact the coefficients are complex numbers with nonzero imaginary parts is relevant. Why?

Hurkyl said:
You posed your question as if the fact the coefficients are complex numbers with nonzero imaginary parts is relevant. Why?

I didn't understand what you said.

It's just algebra, you have two equations in two unknowns. You can solve for Ix in terms of Iy and then do substitution.

The complex coefficients you have represent the reactive components in your circuit, if they don't end up canceling then your currents will be out of phase with your voltage and how far out they are will be determined by the angle you get when you change your answers to polar form.

Can't we solve it by separating the real and imaginary parts both on the left and right hand side of the equation?

sonutulsiani said:
Ix and Iy are currents. Do you know how to solve?

I don't know about currents...all I'm asking whether they are numbers (here variables) or not. If they are just variables (I would like x instead of Ix and y instead of Iy), then it is very easy to solve. (No need to separation). I'm finding the value of Ix below and hope you will be able to follow:

(equation 1).(2i)-(equation 2). (-4i) gives

Ix=[20i]/[(3+4i).2i+(2-4i).4i]=[10]/[(3+4i)+4-8i]=10/(7-4i)=10(7+4i)/(49+16)=(14/13)+(8/13)i

Please check, I may have done any silly mistake in calculation.

Regards,

## 1. How do I solve a system of two equations involving complex variables?

Solving a system of two equations involving complex variables is similar to solving a system of two equations with real numbers. You can use the same techniques such as substitution or elimination to solve the equations. However, when working with complex numbers, it is important to remember to treat the imaginary component (i) as a variable and follow the rules of complex arithmetic.

## 2. What are the common methods used for solving equations with complex variables?

The most common methods for solving equations with complex variables are substitution, elimination, and graphing. These methods are similar to the ones used for solving equations with real numbers, but they must be adapted to account for the imaginary component in complex numbers.

## 3. Can I use the quadratic formula to solve equations with complex variables?

Yes, the quadratic formula can be used to solve equations with complex variables. However, it is important to remember that when using the quadratic formula, the discriminant (b^2 - 4ac) must be positive for the equation to have real solutions. If the discriminant is negative, the equation will have complex solutions.

## 4. How do I graph equations with complex variables?

To graph an equation with complex variables, you can plot the points on a complex plane. The x-axis represents the real part of the complex number, and the y-axis represents the imaginary part. Once you have plotted the points, you can connect them to form a line or curve to represent the equation.

## 5. Are there any special rules for solving equations with complex variables?

Yes, there are a few special rules to keep in mind when solving equations with complex variables. For example, when multiplying or dividing complex numbers, you must use the distributive property and FOIL method. Additionally, when taking the square root of a complex number, you must take the square root of both the real and imaginary components separately.

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