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Complex numbers - equations

Hello everybody

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

Equation:

z^{2}=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

Re: Complex numbers - equations

Quote:

Originally Posted by

**Tala** Equation: z^{2}=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 $\displaystyle \sqrt[4]2\exp\left(\frac{-\pi i}{8}\right)~,$ where $\displaystyle \exp(it)=\cos(t)+i\sin(t).$

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Re: Complex numbers - equations

Re: Complex numbers - equations

I would write:

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

Hence:

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

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

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?

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Re: Complex numbers - equations

Re: Complex numbers - equations

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

Re: Complex numbers - equations

Software...But are my results correct ?

Re: Complex numbers - equations