How do I simplify (5i)^5 ?

Question

How do I simplify (5i)^5 ?

Answer 1

I'll do this first:

i⁵ = (i⁴)i = i; because i⁴ = i²i² = (-1)(-1) = 1

Therefore, we have that:

(5i)⁵ = 5⁵i⁵ = 3125i

Hope this helps!

Answer 2

(5^5)(i^5)

3125(i^5)

3125i^5

Answer 3

Remember the pattern with complex numbers:

i^1 = sq.rt. -1

i^2 = -1

i^3 = - (sq.rt. -1)

i^4 = 1

i^5 = i^1 x i^4, = i(i^4),   = i

5 to the power of 5, gives an answer of 3125i