Complex Number System Reals Rationals (fractions, decimals) Integers (…, -1, -2, 0, 1, 2, …) Whole (0, 1, 2, …) Natural (1, 2, …) Irrationals (no fractions) pi, e Imaginary i, 2i, -3-7i, etc.

Divide the exponent by 4 No remainder: answer is 1. Remainder of.25: answer is i. Remainder of.50: answer is –1. Remainder of.75: answer is –i.

Powers of i Find i 23 Find i 2006 Find i 37 Find i 828

Express these numbers in terms of i

Express these numbers in terms of i.

a + bi Complex Numbers real imaginary The complex numbers consist of all sums a + bi, where a and b are real numbers and i is the imaginary unit. The real part is a, and the imaginary part is bi.

Add or Subtract Complex Numbers (is like combining like terms)

Write the expression as a complex number in standard form

**When subtracting, remember to distribute the subtraction sign, just like you did with polynomials!**

What in the WORLD does it all mean?!? *Solve the following for x.

Multiplying Complex Numbers Treat the i’s like variables, then change any that are not to the first power Ex:

Dividing Complex Numbers Multiply by the conjugate of 5i, which is (-5i) Conjugate: Changing the sign of the imaginary part of a complex number. The Conjugate of a + bi is a – bi.

Dividing Complex Numbers