How do you calculate $\frac{3 ({cos 14}^{\circ} + i {sin 14}^{\circ})}{2 ({cos 121}^{\circ} + i {sin 121}^{\circ})}$ $(3(cos14^circ+isin14^circ))/(2(cos121^circ+isin121^circ)$ ?

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How do you calculate $\frac{3 ({cos 14}^{\circ} + i {sin 14}^{\circ})}{2 ({cos 121}^{\circ} + i {sin 121}^{\circ})}$ $(3(cos14^circ+isin14^circ))/(2(cos121^circ+isin121^circ)$ ?

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Answer 1 · 2017-03-22T15:04:32

$\frac{3 ({cos 14}^{\circ} + i {sin 14}^{\circ})}{2 ({cos 121}^{\circ} + i {sin 121}^{\circ})} = \frac{3}{2} ({cos 107}^{\circ} - i {sin 107}^{\circ})$ $(3(cos14^@+isin14^@))/(2(cos121^@+isin121^@))=3/2(cos107^@-isin107^@)$

Explanation:

$\frac{3 ({cos 14}^{\circ} + i {sin 14}^{\circ})}{2 ({cos 121}^{\circ} + i {sin 121}^{\circ})}$ $(3(cos14^@+isin14^@))/(2(cos121^@+isin121^@)$

= $\frac{3}{2} \times \frac{({cos 14}^{\circ} + i {sin 14}^{\circ})}{({cos 121}^{\circ} + i {sin 121}^{\circ})} \times \frac{({cos 121}^{\circ} - i {sin 121}^{\circ})}{({cos 121}^{\circ} - i {sin 121}^{\circ})}$ $3/2xx((cos14^@+isin14^@))/((cos121^@+isin121^@))xx((cos121^@-isin121^@))/((cos121^@-isin121^@)$

= $\frac{3}{2} \frac{{cos 14}^{\circ} {cos 121}^{\circ} - i^{2} {sin 14}^{\circ} {sin 121}^{\circ} - i {cos 14}^{\circ} {sin 121}^{\circ} + i {sin 14}^{\circ} {cos 121}^{\circ}}{{cos}^{2} 121^{\circ} - i^{2} {sin 121}^{\circ}}$ $3/2(cos14^@cos121^@-i^2sin14^@sin121^@-icos14^@sin121^@+isin14^@cos121^@)/(cos^2 121^@-i^2sin121^@)$

= $\frac{3}{2} \frac{{cos 14}^{\circ} {cos 121}^{\circ} + {sin 14}^{\circ} {sin 121}^{\circ} + i ({sin 14}^{\circ} {cos 121}^{\circ} - {cos 14}^{\circ} {sin 121}^{\circ})}{{cos}^{2} 121^{\circ} + {sin 121}^{\circ}}$ $3/2(cos14^@cos121^@+sin14^@sin121^@+i(sin14^@cos121^@-cos14^@sin121^@))/(cos^2 121^@+sin121^@)$

= $\frac{3}{2} \frac{cos (14^{\circ} - 121^{\circ}) + i sin (14^{\circ} - 121^{\circ})}{1}$ $3/2(cos(14^@-121^@)+isin(14^@-121^@))/1$

= $\frac{3}{2} (cos (- 107^{\circ}) + i sin (- 107^{\circ}))$ $3/2(cos(-107^@)+isin(-107^@))$

= $\frac{3}{2} ({cos 107}^{\circ} - i {sin 107}^{\circ})$ $3/2(cos107^@-isin107^@)$

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How do you calculate $\frac{3 ({cos 14}^{\circ} + i {sin 14}^{\circ})}{2 ({cos 121}^{\circ} + i {sin 121}^{\circ})}$ $(3(cos14^circ+isin14^circ))/(2(cos121^circ+isin121^circ)$ ?

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