Algebra Problem:

Question

Simplify: 4i⁴ - 3i³ - √-3(√3)

(A) 3 - 3i³ + 4i⁴

(B) 7 + 3i

(C) 4 - 6i

(D) 4i

(E) None of the above

For this I got; (E) None of the above. Is this correct?

Answer 1

Jesset, that’s what I get, too.

Answer 2

i = i

i² = -1

i³ = -i

i⁴ = 1

so 4i⁴ = 4(1) = 4

and - 3i³ = (-3)(-i) = + 3i

Also: √-3 = √(-1•3) = √-1•√3 = i√3

So - √-3(√3) = - i√3(√3) but √3•√3 = 3 so it becomes -3i

Summarizing, the expression simplifies to 4 + 3i - 3i = 4 so you are correct