How do you write the trigonometric form in complex form $6 (cos (\frac{5 π}{6}) + i sin (\frac{5 π}{6})))$ $6(cos((5pi)/6)+isin((5pi)/6)))$ ?

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How do you write the trigonometric form in complex form $6 (cos (\frac{5 π}{6}) + i sin (\frac{5 π}{6})))$ $6(cos((5pi)/6)+isin((5pi)/6)))$ ?

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Answer 1 · 2016-10-29T12:26:03

THe complex form is $- 3 \sqrt{3} + 3 i$ $-3sqrt3+3i$

Explanation:

The trigonometric form is $z = r (cos θ + i sin θ)$ $z=r(costheta+isintheta)$
The complex form is $z = a + i b$ $z=a+ib$
so we have to put the values of $cos θ$ $costheta$ and $sin θ$ $sintheta$
$cos (\frac{5 π}{6}) = - cos (\frac{π}{6}) = - \frac{\sqrt{3}}{2}$ $cos((5pi)/6)=-cos( pi/6)=-sqrt3/2$
and $sin (\frac{5 π}{6}) = sin (\frac{π}{6}) = \frac{1}{2}$ $sin((5pi)/6)=sin(pi/6)=1/2$

So we have $z = 6 ((- \frac{\sqrt{3}}{2}) + \frac{i}{2}) = - 3 \sqrt{3} + 3 i$ $z=6((-sqrt3/2)+i/2)=-3sqrt3+3i$

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How do you write the trigonometric form in complex form $6 (cos (\frac{5 π}{6}) + i sin (\frac{5 π}{6})))$ $6(cos((5pi)/6)+isin((5pi)/6)))$ ?

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How do you write the trigonometric form in complex form 6(cos((5pi)/6)+isin((5pi)/6)))6(cos(5π6)+isin(5π6)))6(cos((5pi)/6)+isin((5pi)/6)))?

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Explanation:

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How do you write the trigonometric form in complex form $6 (cos (\frac{5 π}{6}) + i sin (\frac{5 π}{6})))$ $6(cos((5pi)/6)+isin((5pi)/6)))$ ?