Question

There is more than one answer and I really don't understand this concept as a whole.

Answer 1

We first need to remember what is the complex plane:

then they ask us to locate where are the cube roots of 8i, let's find them:

Write 8i in the polar form

8i= (2^3)(cos π/2 +i.sin π/2), its cube roots are 2(cos π/6 +i.sin π/6),

2[cos((π/6)+(2π/3))+i.sin((π/6)+(2π/3))], and

2[cos((π/6)+(4π/3))+i.sin((π/6)+(4π/3))], i.e.

√3 +i, -√3+i and -2i.

then the correct options are "on imaginary axis" (because of -2i); quadrant 1 (because of √3 +i); and quadrant 2 (because of -√3 +i)