# Thread: Complex numbers - equations

1. ## Complex numbers - equations

Hello everybody

I need someone to check whether my results are correct or incorrect:

Equation:

z2=1-i

My results are attached as an image. I think the results are wrong but the problems is that I've used the correct method. it would be really nice if someone could tell me whether the results are correct or incorrect.

Thank you

2. ## Re: Complex numbers - equations

Originally Posted by Tala
Equation: z2=1-i
I think the results are wrong but the problems is that I've used the correct method. it would be really nice if someone could tell me whether the results are correct or incorrect.
When you say "I've used the correct method", what do you mean?

One root is $\sqrt[4]2\exp\left(\frac{-\pi i}{8}\right)~,$ where $\exp(it)=\cos(t)+i\sin(t).$

3. ## Re: Complex numbers - equations

This is what I've done:

4. ## Re: Complex numbers - equations

I would write:

$z^2=1-i=\sqrt{2}\left(\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}i \right)=\sqrt{2}e^{\left(\frac{7\pi}{4} \right)i}$

Hence:

$z=\pm\sqrt[4]{2}e^{\left(\frac{7\pi}{8} \right)i}$

Now you may use Euler's formula to find the rectangular form.

5. ## Re: Complex numbers - equations

Originally Posted by Tala
This is what I've done:
Those are correct.
But where did you get the numbers in the OP?

6. ## Re: Complex numbers - equations

I just multiplied...

7. ## Re: Complex numbers - equations

Did you use software or half-angle identities to evaluate the trig. functions?

8. ## Re: Complex numbers - equations

Software...But are my results correct ?

9. ## Re: Complex numbers - equations

Yes, they are correct.