How do you write the trigonometric form in complex form $\frac{3}{2} (cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3})))$ $3/2(cos((5pi)/3)+isin((5pi)/3)))$ ?

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How do you write the trigonometric form in complex form $\frac{3}{2} (cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3})))$ $3/2(cos((5pi)/3)+isin((5pi)/3)))$ ?

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Answer 1 · 2016-10-04T07:27:03

$\frac{3}{2} (cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3})) = \frac{3}{4} - i \frac{3 \sqrt{3}}{4}$ $3/2(cos((5pi)/3)+isin((5pi)/3))=3/4-i(3sqrt3)/4$

Explanation:

As $cos (\frac{5 π}{3}) = cos (2 π - \frac{π}{3}) = cos (- \frac{π}{3}) = cos (\frac{π}{3}) = \frac{1}{2}$ $cos((5pi)/3)=cos(2pi-pi/3)=cos(-pi/3)=cos(pi/3)=1/2$

and $sin (\frac{5 π}{3}) = sin (2 π - \frac{π}{3}) = sin (- \frac{π}{3}) = - sin (\frac{π}{3}) = - \frac{\sqrt{3}}{2}$ $sin((5pi)/3)=sin(2pi-pi/3)=sin(-pi/3)=-sin(pi/3)=-sqrt3/2$

Hence $\frac{3}{2} (cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3}))$ $3/2(cos((5pi)/3)+isin((5pi)/3))$

= $\frac{3}{2} (\frac{1}{2} - i \frac{\sqrt{3}}{2})$ $3/2(1/2-isqrt3/2)$

= $\frac{3}{4} - i \frac{3 \sqrt{3}}{4}$ $3/4-i(3sqrt3)/4$

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How do you write the trigonometric form in complex form $\frac{3}{2} (cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3})))$ $3/2(cos((5pi)/3)+isin((5pi)/3)))$ ?

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Explanation:

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How do you write the trigonometric form in complex form $\frac{3}{2} (cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3})))$ $3/2(cos((5pi)/3)+isin((5pi)/3)))$ ?