Perform Operations with Complex Numbers Section 4.6 Perform Operations with Complex Numbers

California Standard: 6.0: Students add, subtract, multiply, and divide complex numbers 5.0: Students demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically. In particular, they can plot complex numbers as points in the plane.

By following instructions, students will be able to: OBJECTIVE(S): By following instructions, students will be able to: Perform operations with complex numbers.

Def: an imaginary unit is defined by: Furthermore,

EXAMPLE 1: Solve .

U-TRY#1: Solve the equation. c) b) d) 6

Def: complex number is a number a+bi where a is a real number and bi is imaginary.

EXAMPLE 2: Write the expression as a complex number in standard form. a) b) c)

U-TRY#2: Write the expression as a complex number in standard form. c) 9

EXAMPLE 3: Write the expression as a complex number in standard form. a) b)

Def: complex conjugates – two complex numbers of the form a+bi and a-bi are complex conjugates Example: (2+4i)(2-4i) (3+5i)(3-5i)

EXAMPLE 4: Write the quotient in standard form.

U-TRY#3: Write the expression as a complex number in standard form. c) b) d) 13

EXAMPLE 5: Plot the complex numbers in the same complex plane. a) b) c) d)

Absolute Value of a Complex Number– the absolute value of a complex number z=a+bi is denoted by |z|, is a nonnegative real number defined as

EXAMPLE 6: Find the absolute value of: a) b)

U-TRY#4: Plot the complex numbers in the same complex plane. Then find the absolute value of each complex number. c) b) d) 17

HOMEWORK Sec 4.6 WS