Question

Which expression is a CUBE ROOT of -2i?

Answer 1

remember
∛(ab)=(∛a)(∛b)

also
i¹=i
i²=-1
i³=-i
i⁴=1

so

∛-2i=(∛2)(∛-i)=(∛2)(i)=i∛2

Answer 2

i√(2i)

Explanation:

Imaginary numbers are complex numbers which can be represented as real numbers by multiplying them with imaginary unit (i = √-1). -2i is an imaginary number. Heron of Alexandria is thought of to be the first person to have used imaginary numbers.

Cube root of -2i

√-2i

= i√2i

= -8×(√-1)³

= i√2i

= i√2i

√-2i

= i√2i

∴ The expression is a CUBE ROOT of -2i is i√(2i)