Product of Complex Numbers in Polar Form/Examples/3 cis 40 x 4 cis 80
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Example of Use of Product of Complex Numbers in Polar Form
- $3 \cis 40 \degrees \times 4 \cis 80 \degrees = -6 + 6 \sqrt 3 i$
Proof
\(\ds 3 \cis 40 \degrees \times 4 \cis 80 \degrees\) | \(=\) | \(\ds \paren {3 \times 4} \map \cis {40 \degrees + 80 \degrees}\) | Product of Complex Numbers in Polar Form | |||||||||||
\(\ds \) | \(=\) | \(\ds 12 \cis 120 \degrees\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 12 \paren {\cos 120 \degrees + i \sin 120 \degrees}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 12 \times \paren {-\dfrac 1 2} + 12 i \paren {\dfrac {\sqrt 3} 2}\) | Cosine of $120 \degrees$, Sine of $120 \degrees$ | |||||||||||
\(\ds \) | \(=\) | \(\ds -6 + 6 \sqrt 3 i\) | simplifying |
$\blacksquare$
Sources
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Solved Problems: De Moivre's Theorem: $26 \ \text {(a)}$