How do you multiply $e^{\frac{3 π}{8} i} \cdot e^{\frac{π}{2} i}$ $e^(( 3 pi )/ 8 i) * e^( pi/2 i )$ in trigonometric form?

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How do you multiply $e^{\frac{3 π}{8} i} \cdot e^{\frac{π}{2} i}$ $e^(( 3 pi )/ 8 i) * e^( pi/2 i )$ in trigonometric form?

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Answer 1 · 2018-04-28T06:16:26

Well, we knkw that $e^{i θ} = cos θ + i sin θ$ $e^(itheta)=costheta+isintheta$

And that $e_{1}^{i θ_{1}} \cdot e_{2}^{i θ_{2}} = e^{i (θ_{1} + θ_{2})} = cos (θ_{1} + θ_{2}) + i sin (θ_{1} + θ_{2})$ $e^(itheta_1)*e^(itheta_2)=e^(i(theta_1+theta_2))=cos(theta_1+theta_2)+isin(theta_1+theta_2)$

$\frac{3 π}{8} + \frac{π}{2} = \frac{7 π}{8}$ $(3pi)/8+pi/2=(7pi)/8$

$cos (\frac{7 π}{8}) + i sin cos (\frac{7 π}{8}) = \frac{\sqrt{2 + \sqrt{2}}}{2} + \frac{\sqrt{2 - \sqrt{2}}}{2} i \approx 0.92 + 0.38 i$ $cos((7pi)/8)+isincos((7pi)/8)=sqrt(2+sqrt2)/2+sqrt(2-sqrt2)/2i~~0.92+0.38i$

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How do you multiply $e^{\frac{3 π}{8} i} \cdot e^{\frac{π}{2} i}$ $e^(( 3 pi )/ 8 i) * e^( pi/2 i )$ in trigonometric form?

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