Precalculus - Chapter 6 Trigonometry Worksheet With Answers printable pdf download

Precalculus - Chapter 6 Trigonometry Worksheet With Answers

PRECALCULUS

Name______________________

Chapter 6: Additional Topics in Trigonometry

Date____________ Period______

Example 1: Find the Absolute Value of a Complex Number

6.5 – Trig Form of a Complex Number

Plot z = 3 – 4i and find its absolute value.

• Plot complex numbers in the complex plane and find absolute

values of complex numbers.

• Write trigonometric forms of complex numbers.

• Multiply and divide complex numbers written in

trigonometric form.

• Use DeMoivre’s Theorem to find powers of complex

numbers.

• Find nth roots of complex numbers.

I. - INTRODUCTION

You can represent a complex number z = a + bi as the point

II. – TRIG FORM OF A COMPLEX NUMBER

(a,b) in a coordinate plane (called the complex plane). The

horizontal axis is the real axis and the vertical axis is the imaginary

Consider the picture to the right.

axis.

You can write

a = r cos θ and b = r sin θ.

Consequently you get

a + bi = (r cos θ) + (r sin θ)i

The absolute value of a complex number a + bi is defined

as the distance between the origin (0,0) and the point (a,b).

• The trigonometric form of a complex number is called the

POLAR FORM.

Precalculus - Chapter 6 Trigonometry Worksheet With Answers