Question

How do I simplify the following to "a+bi" form: (1+2i)^3

Answer 1

Answer:

Expand it.

(1+2i)^3 is equal to (1+2i)(1+2i)(1+2i).

Multiply everything out (being sure to multiply every term. (1+2i) * (1+2i) = 1+2i+2i+4i^2.

i is the square root of negative one, so i^2 is just -1. 1+2i+2i-4 is what you get from the first two, so now simplify that:

1-4 + 2i+2i = (-3+4i) and now multiply that by (1+2i):

(-3+4i) * (1+2i) = -3 - 6i +4i +8i^2.

Simplify again, and the answer is: -11-2i

Step-by-step explanation:

I hope this helps - really my only tip is don't spend time thinking about what i is, that just hurts your brain. Just remember that i^2 is equal to negative one, and treat it like regular multiplication and you will be fine.