Polar Form of Complex Number/Examples/4 cis 3 pi 5^-1

Example of Polar Form of Complex Number

The complex number $4 \paren {\cos \dfrac {3 \pi} 5 + i \sin \dfrac {3 \pi} 5}$ can be expressed as:

$4 \paren {\cos \dfrac {3 \pi} 5 + i \sin \dfrac {3 \pi} 5} = 4 \paren {\cos 108 \degrees + i \sin 108 \degrees} = 6 \cis 108 \degrees = 6 \cis \dfrac {3 \pi} 5 = 6 e^{3 \pi / 5}$

and depicted in the complex plane as:

Sources

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