Polar Form of Complex Number/Examples/6 cis 135
Jump to navigation
Jump to search
Example of Polar Form of Complex Number
The complex number $\polar {6, 135 \degrees}$ can be expressed in Cartesian form as:
- $6 \cis 135 \degrees = -3 \sqrt 2 + 3 \sqrt 2 i$
and depicted in the complex plane as:
Proof
\(\ds 6 \cis 135 \degrees\) | \(=\) | \(\ds 6 \paren {\cos 135 \degrees + i \sin 135 \degrees}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 6 \times \dfrac {-\sqrt 2} 2 + 6 i \times \dfrac {\sqrt 2} 2\) | Cosine of $135 \degrees$ and Sine of $135 \degrees$ | |||||||||||
\(\ds \) | \(=\) | \(\ds -3 \sqrt 2 + 3 \sqrt 2 i\) |
$\blacksquare$
Sources
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: Polar Form of Complex Numbers: $84 \ \text {(a)}$