SOLUTION: Find all complex solutions to the equation z^4 = -64 - 16z^2. Enter all the solutions in the form $a + bi$, where $a$ and $b$ are real numbers.

Question 1209643: Find all complex solutions to the equation z^4 = -64 - 16z^2.

Enter all the solutions in the form $a + bi$, where $a$ and $b$ are real numbers.
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
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Find all complex solutions to the equation z^4 = -64 - 16z^2.
Enter all the solutions in the form a + bi, where a and b are real numbers.
~~~~~~~~~~~~~~~~~~~~~~~~~~~

An equation

    z^4 = -64 - 16z^2

is equivalent to

    z^4 + 16z^2 + 64 = 0,

     = 0.


Over complex numbers, the last equation can be factored

     = 0,

or

     = 0.


It means that the given equation has these 4 roots

    z =   of the multiplicity 2,  and  z =   of the multiplicity 2.    ANSWER

Solved.

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