Imaginary And Complex Numbers

Introduction

So just trying to keep this stuff in my head. 42 years ago I was onto all this so let's see how we go. From memory is was a pretty easy ride. Just remember   $i=\sqrt{-1}$   $i^2=-1$   $i^3=1$   $i^4=1$

Simplifying

So he gave examples and how he solved it an I guess most of the was just substitution and recognizing you can split exponent by adding e.g. $x^4=x^3.x^1$
So
  $i^7=i^4.i^3$ = $1.(-i)$ = i
  $i^{3}3=i^{3}2.i^1$ = $(1^4{)}^8.i$ = $i^8.i$ = i