How do you write the trigonometric form in complex form $8 (cos (\frac{π}{6}) + i sin (\frac{π}{6})))$ $8(cos((pi)/6)+isin((pi)/6)))$ ?

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Answer 1 · 2016-11-28T17:32:07

The answer is $= \frac{\sqrt{3}}{4} + \frac{i}{4}$ $=sqrt3/4+i/4$

We calculate

$cos (\frac{π}{6}) = \frac{\sqrt{3}}{2}$ $cos(pi/6)=sqrt3/2$

$sin (\frac{π}{6}) = \frac{1}{2}$ $sin(pi/6)=1/2$

Therefore,

$z = 8 (cos (\frac{π}{6}) + i (sin (\frac{π}{6}))$ $z=8(cos(pi/6)+i(sin(pi/6))$

$= 8 (\frac{\sqrt{3}}{2} + i \cdot \frac{1}{2})$ $=8(sqrt3/2+i*1/2)$

$= \frac{\sqrt{3}}{4} + \frac{i}{4}$ $=sqrt3/4+i/4$

How do you write the trigonometric form in complex form 8(cos(π6)+isin(π6)))8(cos((pi)/6)+isin((pi)/6)))?