De Moivre’s Theorem and nth Roots 6.6 De Moivre’s Theorem and nth Roots

What you’ll learn about The Complex Plane Trigonometric Form of Complex Numbers Multiplication and Division of Complex Numbers Powers of Complex Numbers Roots of Complex Numbers … and why The material extends your equation-solving technique to include equations of the form zn = c, n is an integer and c is a complex number.

Complex Plane

Absolute Value (Modulus) of a Complex Number

Graph of z = a + bi

Trigonometric Form of a Complex Number

Example Finding Trigonometric Form

Example Finding Trigonometric Form

Product and Quotient of Complex Numbers

Example Multiplying Complex Numbers

Example Multiplying Complex Numbers

A Geometric Interpretation of z2

De Moivre’s Theorem

Example Using De Moivre’s Theorem

Example Using De Moivre’s Theorem

Example Using De Moivre’s Theorem

nth Root of a Complex Number

Finding nth Roots of a Complex Number

Example Finding Cube Roots

Example Finding Cube Roots