You could rewrite the equation as:
Hi everyone
I'm trying to solve this equation:
z^{4}+1 = 0
I've tried every method I can think of, such as De Moivre's formula, but I only get two complex roots.
What method do I use ?
I just want to know the method/procedure.
We have:
We find: hence, we may state:
So, we must have:
where
By Euler's formula, we know then:
Now, we want:
Since k is an integer, we have
Hence, we have:
Now, use the values we found for k to compute the 4 roots.