Polar Form of Complex Number/Examples/2 cis -pi 4^-1

Example of Polar Form of Complex Number

The complex number $2 \paren {\cos \dfrac {-\pi} 4 + i \sin \dfrac {-\pi} 4}$ can be expressed as:

$4 \paren {\cos \dfrac {-\pi} 4 + i \sin \dfrac {-\pi} 4} = 2 \paren {\cos 315 \degrees + i \sin 315 \degrees} = 2 \cis 315 \degrees = 2 \cis \dfrac {-\pi} 4 = 2 e^{-\pi / 4}$

and depicted in the complex plane as:

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Solved Problems: Polar Form of Complex Numbers: $17 \ \text {(c)}$