What type of equation is this? How to solve it?

Question

$$m^4+a^4=0$$ , the answer I obtained is $$0+i1,0-i1$$ but the answer is given as a/sqrt(2)-a/sqrt(2),a/sqrt(2)+a/sqrt(2)

Answer 1

Hint: $$m^4+a^4+2m^2a^2-2m^2a^2=0$$

$$(m^2+a^2)^2-2m^2a^2=0$$, Now apply $(a^2-b^2)=(a+b)(a-b)$

then it will reduces in 2-degree polynomials. Next apply "Shri Dhar Acharya Rule"

Answer 2

We have: $\left(\dfrac{m}{a}\right)^4 = - 1$. Thus: let $y = \dfrac{m}{a}$, then $y^4 = - 1$. Thus $y$ is the $4th$ roots of $-1$, and you can list all the roots using Demoivre'theorem, then you solve for $m$.