5-65-6Complex NumbersComplex Numbers

Part 1Part 1Big Idea: Identify and graph complex numbers.

Imaginary NumbersImaginary NumbersImaginary numbers are

represented by .

Imaginary numbers are defined as the number whose square is -1. So and

Imaginary numbers are of the form of a + bi where a and b are real numbers and b 0.

i 1

Ex 1Ex 1: Simplify each number by : Simplify each number by using imaginary number i.using imaginary number i.A) B)

C) D) -

49 25

200 75

E) F) 1005 166

Complex NumbersComplex Numbers

Ex 2Ex 2: Write each number in the : Write each number in the form of a + bi.form of a + bi.A) B)

C) D)

54 1032

46 172

E) F) 1255 366

Complex Plane

Absolute value of a complex Absolute value of a complex numbernumber

22 babia

Ex 3Ex 3: Find the absolute value of : Find the absolute value of each complex number.each complex number.A) B)

C) D)

i5 i8

i31 i25

Ex 4Ex 4: Simplify each expression.: Simplify each expression.A) (5 – 2i)+ (-3 +i)

B) (-7 + 3i) +(-4 – 4i)

C) (6 + 10i) + (-6i)

D) 7 - (9 - 4i)