Complex Numbers Write imaginary numbers using i. 2.Perform arithmetic operations with complex numbers. 3.Raise i to powers.

Imaginary unit: Imaginary number: A number that can be expressed in the form bi, where b is a real number and i is the imaginary unit.

Complex number: A number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit. Examples: real imaginary

Complex Numbers: a + bi b = 0: Real numbers a = 0: Imaginary numbers realimaginary

Add Complex Numbers Add the real parts – add the imaginary parts

Subtract Complex Numbers

Slide Copyright © 2011 Pearson Education, Inc. Simplify. (  4 + 7i) – (2 + i) a) 2 + 7i 2 b) 2 + 8i c)  6 + 6i d)  6 + 8i

Slide Copyright © 2011 Pearson Education, Inc. Simplify. (  4 + 7i) – (2 + i) a) 2 + 7i 2 b) 2 + 8i c)  6 + 6i d)  6 + 8i

Multiply Complex Numbers

standard a + bi form

Multiply Complex Numbers

Rewrite & Foil

Slide Copyright © 2011 Pearson Education, Inc. Multiply. (  4 + 7i)(2 + i) a)  i b) i c)  i d) i

Slide Copyright © 2011 Pearson Education, Inc. Multiply. (  4 + 7i)(2 + i) a)  i b) i c)  i d) i

Divide Complex Numbers

Binomial denominator conjugate Divide Complex Numbers standard a + bi form

Slide Copyright © 2011 Pearson Education, Inc. Write in standard form. a) b) c) d)

Slide Copyright © 2011 Pearson Education, Inc. Write in standard form. a) b) c) d)

Powers of i:

Simplify: