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Find all complex numbers z such that z^4 = -4 Note: All solutions should be expressed in the form a+bi, where a and b are real numbers. Please use Simons favorite factoring trick thank you!

 Sep 18, 2022
 #1
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I'll use Sophie Germain's Identity for this problem and don't think it would be posssible to use the Simon's favorite factoring trick. The Simon's favorite factoring trick is only applicable in:

- Two variable problems

- Degree of no more than 2. 

 

z^4 + 4(1^4) = (z^2 + 2z + 2)(z^2 - 2z + 2)

 

You can find the complex roots by using the quadratic formula from there.

 

For this problem, you can even use Roots of Unity: https://artofproblemsolving.com/wiki/index.php/Roots_of_unity.

 Sep 18, 2022

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