Algebra and Trigonometry, 5th Edition

8.3 Complex Numbers: Trigonometric Notation

• Graph complex numbers.

• Given a complex number in standard notation, find trigonometric, or polar, notation; and given a complex number in trigonometric notation, find standard notation.

• Use trigonometric notation to multiply and divide complex numbers.

• Use DeMoivre’s theorem to raise complex numbers to powers.

• Find the nth roots of a complex number.

Graphical Representation

JUST IN TIME 1

Just as real numbers can be graphed on a line, complex numbers can be graphed on a plane. We graph a complex number $a+bi$ in the same way that we graph an ordered pair of real numbers $\left(a,b\right)$. However, in place of an x-axis, we have a real axis, and in place of a y-axis, we have an imaginary axis. Horizontal ...