# Complex numbers - equations

• Sep 29th 2012, 06:57 AM
Tala
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
• Sep 29th 2012, 07:15 AM
Plato
Re: Complex numbers - equations
Quote:

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 $\exp(it)=\cos(t)+i\sin(t).$
• Sep 29th 2012, 07:25 AM
Tala
Re: Complex numbers - equations
This is what I've done:
• Sep 29th 2012, 07:26 AM
MarkFL
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.
• Sep 29th 2012, 07:32 AM
Plato
Re: Complex numbers - equations
Quote:

Originally Posted by Tala
This is what I've done:

Those are correct.
But where did you get the numbers in the OP?
• Sep 29th 2012, 07:40 AM
Tala
Re: Complex numbers - equations
I just multiplied...
• Sep 29th 2012, 07:49 AM
MarkFL
Re: Complex numbers - equations
Did you use software or half-angle identities to evaluate the trig. functions?
• Sep 29th 2012, 07:50 AM
Tala
Re: Complex numbers - equations
Software...But are my results correct ?
• Sep 29th 2012, 08:24 AM
MarkFL
Re: Complex numbers - equations
Yes, they are correct.