Polar Form and its Applications MTH 324 Lecture # 2 Polar Form and its Applications

Previous Lecture’s Review The real number system The complex number system Comparison of real system with complex system

Lecture’s outline Polar Form of complex number Powers and roots Comparison with Real analysis

Complex number as a vector

Modulus Properties

Triangle Inequality Proof.

Set of points in the complex plane Example

Polar Form

Cont… Remark

Example: Solution:

Example: Solution:

Principal Argument Notation Example

De Moivre’s Formula Applications: To find power of complex number To find roots of a non-zero complex number

Example: Solution:

Comparison of Real system with Complex Roots of a complex number are also complex whereas the roots of a real number are not necessarily real.

References A First Course in Complex Analysis with Applications by Dennis G. Zill and Patrick D. Shanahan.