Solve the Complex Numbers equation

[TheRedDevil18]

Homework Statement

Solve the following complex equation for z:

zⁱ = sqrt(3) - i

Homework Equations

The Attempt at a Solution

Do I have to equate the real and imaginary parts ?, this is what I tried

zⁱ = (x+iy)ⁱ = exp(i*log(x+iy))

 

[ehild]

I suggest to use the exponential form.

ehild

 

[TheRedDevil18]

I suggest to use the exponential form.

ehild

I'm not sure what form that is. I tried doing it this way but it gets very messy and I don't think it works out

 

[GFauxPas]

The polar, or exponential, form of a complex number is z = |z| e^{i arg z}, did you learn that?

Also, 2 = e^ln2

 

[Ray Vickson]

I'm not sure what form that is. I tried doing it this way but it gets very messy and I don't think it works out

Nevertheless, show us what you obtained, messy or not. Anyway, the answer should be messy.

 

[TheRedDevil18]

The polar, or exponential, form of a complex number is z = |z| e^{i arg z}, did you learn that?

Also, 2 = e^ln2

I tried it and I got up to this stage

(|z| e^{i arg z})ⁱ
= zⁱ e^{-arg z}
= e^{I lnz} e^{-arg z}

And, I'm stuck

 

[ehild]

You can do something with the other side, too. Write it in exponential form.

ehild