So the equation is $$\frac{z^4}{i^{15}+i^{80}}=-1$$
I`ve tried to solve it by this way $$z^4+iz^4=-2$$ => $$(1+i)z^4=-2$$ then I multiplied both sides by $$(1+i) => z^4=-1+i$$ From this I have $$\sqrt{2}e^{i(3\pi/4)} = z^4.$$
Then I got $$(2)^\frac{1}{8}e^i\frac{3\pi}{16}$$
which means that the roots is $$(2)^{\frac{1}{8}e^{i2k}\frac{pi}{4}+\frac{3pi}{16}}$$ How I can express the solution in exponential form and plot on the complex plane
