1. Notes 9-5: Simplifying Complex Numbers
a + bi is a complex number in rectangular form where a and b are real numbers and i is an imaginary number.
Reminder: 1 i
repeating pattern
(cycle of 4 values) -1 -i 1

2. To simplify imaginary numbers with exponents, it is often useful to divide the exponent by 4 and then look at the value of the remainder:
so your answer is:
remainder:
(after dividing by 4)
corresponds to:

3. Examples: i -1

4. turn it into a positive value.-1
What do we do with a negative remainder?
Add one “cycle” of 4 to
turn it into a positive value.
remainder -1 is the same as = remainder 3