Product of Complex Numbers in Polar Form/Examples/5 cis 20 x 3 cis 40
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Example of Use of Product of Complex Numbers in Polar Form
- $5 \cis 20 \degrees \times 3 \cis 40 \degrees = \dfrac {15} 2 + \dfrac {15 \sqrt 3} 2 i$
Proof
\(\ds 5 \cis 20 \degrees \times 3 \cis 40 \degrees\) | \(=\) | \(\ds \paren {5 \times 3} \, \map \cis {20 \degrees + 40 \degrees}\) | Product of Complex Numbers in Polar Form | |||||||||||
\(\ds \) | \(=\) | \(\ds 15 \cis 60 \degrees\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 15 \paren {\cos 60 \degrees + i \sin 60 \degrees}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 15 \times \paren {\dfrac 1 2} + 15 i \paren {\dfrac {\sqrt 3} 2}\) | Cosine of $60 \degrees$, Sine of $60 \degrees$ | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {15} 2 + \dfrac {15 \sqrt 3} 2 i\) | tidying |
$\blacksquare$
Sources
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: De Moivre's Theorem: $89 \ \text{(a)}$