Definition:Polar Form of Complex Number/Also known as

Polar Form of Complex Number: Also known as

Polar form can also be found as:

• trigonometric form
• modulus-argument form.

As $\cos \theta + i \sin \theta$ appears so often in complex analysis, the abbreviation $\cis \theta$ is frequently seen.

Hence $r \paren {\cos \theta + i \sin \theta}$ can be expressed in the economical form $r \cis \theta$.

Sources

• 1957: E.G. Phillips: Functions of a Complex Variable (8th ed.) ... (previous) ... (next): Chapter $\text I$: Functions of a Complex Variable: $\S 3$. Geometric Representation of Complex Numbers
• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 1$: The Language of Set Theory
• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Polar Form of Complex Numbers
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): complex number
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): complex number