Express sin-5- i 1-cos-5 in polar form-

Sin π/5+i(1 cosπ/5 ) =2 sin π/10 cos π/10+i^2 sin^2 π/10 [Using sin 2θ=2 sin θ cos θ and 1 cos 2θ=2 sin^2θ] =2 sinπ/10(cosπ/10+i sinπ/10) ...

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Euler's Representation

Express sinπ/...

Question

Express $s i n \frac{π}{5} + i (1 - c o s \frac{π}{5})$ in polar form.

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Solution

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Express the complex number $s i n \frac{π}{5} + i (1 - c o s \frac{π}{5})$ in polar form.

The amplitude of
$s i n \frac{π}{5} + i (1 - c o s \frac{π}{5})$

z

z = sin (\frac{π}{5}) + i (1 - cos (\frac{π}{5}))

{⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \frac{sin \frac{π}{6} + i (1 - cos \frac{π}{6})}{sin \frac{π}{6} - i (1 - cos \frac{π}{6})} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦}^{2}

i = \sqrt{- 1}

\sin \frac{π}{5} + i (1 - \cos \frac{π}{5})

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