Question

Expand and simplify. (i represents the imaginary unit)
(3-2i)^7

Answer 1

Please help me!

Answer 2

Simply take \[(3-2i)(3-2i)(3-2i)(3-2i)(3-2i)(3-2i)(3-2i)\]by using FOIL which just means First, Outer, Inner, Last.

I'll multiply the first two together (3-2i)(3-2i) and from there you can build on to that.
First as in 3*3=9
Outer as in 3*-2i=-6i
Inner as in -2i*3=-6i
Last as in -2i*-2i=-4

Then add them all together.
9-6i-6i-4=(5-12i)

You might be thinking, hey, how come -2i times -2i is -4 and not 4i^2? That's because\[i^2=-1\]
Don't forget this. The imaginary unit follows this pattern:\[i^0=1\]\[i^1=i\]\[i^2=-1\]\[i^3=-i\] and then it repeats every 4 powers. So i^4=1

It's a pretty simple pattern to remember as long as you remember that anything to the zeroth power is 1 and anything to the first power is itself. From there, as long as you remember it alternates, you'll know the next two and all others after that by dividing by 4 and finding the remainder.