How to eliminate imaginary parts of complex expression?

[kaizen.moto]

Hi,
I have a problem on how to convert the imaginary parts of expression into all real parts. For example:

x1 = - (a + ib)
x2 = (a + ib)
x3 = - (a - ib)
x4 = (a - ib)

My question is that how to express x1, x2, x3 and x4 in terms of real parts only without imaginary parts. I have used Eulers Formula, De Moivers theorem, polar coordinates to solve this problem but still ending with imaginary parts.

Please help me how to solve this problems.

Many thanks in advance.

 

[chiro]

Hi,
I have a problem on how to convert the imaginary parts of expression into all real parts. For example:

x1 = - (a + ib)
x2 = (a + ib)
x3 = - (a - ib)
x4 = (a - ib)

My question is that how to express x1, x2, x3 and x4 in terms of real parts only without imaginary parts. I have used Eulers Formula, De Moivers theorem, polar coordinates to solve this problem but still ending with imaginary parts.

Please help me how to solve this problems.

Many thanks in advance.

If I think what you're trying to do is find Re(z) where z is the complex variable using a formula, then the only way to find Re(z) without just getting it directly by looking at it, is to use the conjugate.

Re(z) = (z + conjugate(z))/2

If you have the polar coordinates you can simply use

Re(z) = r * cos(theta)

Hope that helps!

 

[HallsofIvy]

Hi,
I have a problem on how to convert the imaginary parts of expression into all real parts. For example:

x1 = - (a + ib)
x2 = (a + ib)
x3 = - (a - ib)
x4 = (a - ib)

My question is that how to express x1, x2, x3 and x4 in terms of real parts only without imaginary parts.

You can't. Because those are complex numbers, they cannot be expressed solely in terms of real numbers. If you mean "express only in terms of a, the real part of each number, you can't do that either because they all depend upon b, the imaginary part.

I have used Eulers Formula, De Moivers theorem, polar coordinates to solve this problem but still ending with imaginary parts.

Please help me how to solve this problems.

Many thanks in advance.

It's not clear what you want to do- you can't write a complex number without using imaginary numbers.

 

[Noesis]

As HallsofIvy said, you can't. You should be clearer with your word choice if you wish to do what chiro referred to.

As per your problem: take a look at the variables and see if you can find the conjugate of each expressed as another variable, and then consider their sum.

 

[CellCoree]

Hello,

Thank you for reaching out with your question. It seems like you are trying to eliminate the imaginary parts of a complex expression. This can be done by using a technique called "conjugation".

To eliminate the imaginary parts, we can use the fact that the product of a complex number and its conjugate is always a real number. The conjugate of a complex number is found by changing the sign of the imaginary part. For example, the conjugate of (a + ib) is (a - ib).

Using this, we can express x1, x2, x3, and x4 in terms of their real parts only by multiplying each expression by its conjugate and simplifying:

x1 = -(a + ib) * (a - ib) = -a^2 - b^2
x2 = (a + ib) * (a - ib) = a^2 + b^2
x3 = -(a - ib) * (a + ib) = -a^2 - b^2
x4 = (a - ib) * (a + ib) = a^2 + b^2

As you can see, all imaginary parts have been eliminated and we are left with only the real parts. I hope this helps you solve your problem. If you have any further questions, please don't hesitate to reach out.

Best of luck!