What is the product of $5 (cos \frac{3 π}{4} + i sin \frac{3 π}{4}) \cdot \sqrt{3} (cos \frac{π}{2} + i sin \frac{π}{2})$ $5 (cos frac{3\pi}{4}+isinfrac{3\pi}{4} ) \cdot \sqrt{3}(cosfrac{\pi}{2}+i sinfrac{\pi}{2})$ ?

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What is the product of $5 (cos \frac{3 π}{4} + i sin \frac{3 π}{4}) \cdot \sqrt{3} (cos \frac{π}{2} + i sin \frac{π}{2})$ $5 (cos frac{3\pi}{4}+isinfrac{3\pi}{4} ) \cdot \sqrt{3}(cosfrac{\pi}{2}+i sinfrac{\pi}{2})$ ?

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Answer 1 · 2018-06-14T04:37:02

$\Rightarrow - 5 \sqrt{\frac{3}{2}} + i 5 \sqrt{\frac{3}{2}}$ $color(maroon)(=> -5sqrt(3/2) + i 5sqrt(3/2)$ or $- 5 \sqrt{\frac{3}{2}} (1 - i)$ $-5sqrt(3/2)(1-i)$

Explanation:

$Z_{1} \cdot Z_{2} = r_{1} \cdot r_{2} (cos (θ_{1} + θ_{2}) + i sin (θ_{1} + θ_{2}))$ $Z_1 * Z_2 = r_1*r_2 (cos (theta_1+ theta_2) + i sin (theta_1 + theta_2))$

$Z_{1} = 5 (cos (\frac{3 π}{4}) + i sin (\frac{3 π}{4})$ $Z_1 = 5 (cos ((3pi)/4) + i sin ((3pi)/4)$

$Z_{2} = \sqrt{3} (cos (\frac{π}{2}) + i sin (\frac{π}{2}))$ $Z_2 = sqrt3 (cos (pi/2) + i sin (pi/2))$

$r_{1} = 5, r_{2} = \sqrt{3}, θ_{1} = \frac{3 π}{4}, θ_{2} = \frac{π}{2}$ $r_1 =5, r_2 = sqrt3, theta_1 = (3pi)/4, theta_2 = pi/2$

$Z_{1} \cdot Z_{2} = 5 \sqrt{3} ((cos (\frac{3 π}{4} + \frac{π}{2}) + i sin (\frac{3 π}{4} + \frac{π}{2}))$ $Z_1 * Z_2 = 5 sqrt3 ((cos ((3pi)/4 + pi/2) + i sin ((3pi)/4 + pi/2))$

$\Rightarrow 5 \sqrt{3} \cdot (- (\frac{1}{\sqrt{2}}) + i (\frac{1}{\sqrt{2}}))$ $=> 5 sqrt3 * (-(1/sqrt2) + i (1/sqrt2))$

$\Rightarrow - 5 \sqrt{\frac{3}{2}} + i 5 \sqrt{\frac{3}{2}}$ $color(maroon)(=> -5sqrt(3/2) + i 5sqrt(3/2)$ or $- 5 \sqrt{\frac{3}{2}} (1 - i)$ $-5sqrt(3/2)(1-i)$

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What is the product of $5 (cos \frac{3 π}{4} + i sin \frac{3 π}{4}) \cdot \sqrt{3} (cos \frac{π}{2} + i sin \frac{π}{2})$ $5 (cos frac{3\pi}{4}+isinfrac{3\pi}{4} ) \cdot \sqrt{3}(cosfrac{\pi}{2}+i sinfrac{\pi}{2})$ ?

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What is the product of $5 (cos \frac{3 π}{4} + i sin \frac{3 π}{4}) \cdot \sqrt{3} (cos \frac{π}{2} + i sin \frac{π}{2})$ $5 (cos frac{3\pi}{4}+isinfrac{3\pi}{4} ) \cdot \sqrt{3}(cosfrac{\pi}{2}+i sinfrac{\pi}{2})$ ?