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Question-121705




Question Number 121705 by bemath last updated on 11/Nov/20
Answered by MJS_new last updated on 11/Nov/20
cis x =cos x +i sin x =e^(ix)   16°=((4π)/(45)); 44°=((11π)/(45)); 62°=((31π)/(90))  ((12e^(((4π)/(45))i) )/(3e^(((11π)/(45))i) 2e^(((31π)/(90))i) ))=2e^(iπ((4/(45))−((11)/(45))−((31)/(90)))) =2e^(−i(π/2)) =−2i
$$\mathrm{cis}\:{x}\:=\mathrm{cos}\:{x}\:+\mathrm{i}\:\mathrm{sin}\:{x}\:=\mathrm{e}^{\mathrm{i}{x}} \\ $$$$\mathrm{16}°=\frac{\mathrm{4}\pi}{\mathrm{45}};\:\mathrm{44}°=\frac{\mathrm{11}\pi}{\mathrm{45}};\:\mathrm{62}°=\frac{\mathrm{31}\pi}{\mathrm{90}} \\ $$$$\frac{\mathrm{12e}^{\frac{\mathrm{4}\pi}{\mathrm{45}}\mathrm{i}} }{\mathrm{3e}^{\frac{\mathrm{11}\pi}{\mathrm{45}}\mathrm{i}} \mathrm{2e}^{\frac{\mathrm{31}\pi}{\mathrm{90}}\mathrm{i}} }=\mathrm{2e}^{\mathrm{i}\pi\left(\frac{\mathrm{4}}{\mathrm{45}}−\frac{\mathrm{11}}{\mathrm{45}}−\frac{\mathrm{31}}{\mathrm{90}}\right)} =\mathrm{2e}^{−\mathrm{i}\frac{\pi}{\mathrm{2}}} =−\mathrm{2i} \\ $$

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