((2∙(cos85° + isin85°))/( (√2)∙(cos40° + isin40°))) = ?


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Question Number 149121 by mathdanisur last updated on 03/Aug/21

$\frac{2 \cdot (c o s 85 ° + i s i n 85 °)}{\sqrt{2} \cdot (c o s 40 ° + i s i n 40 °)} = ?$
	Answered by bramlexs22 last updated on 03/Aug/21

	$\sqrt{2} e^{i (85 ° - 40 °}) = \sqrt{2} e^{i 45 °} = \sqrt{2} (\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2} i)$ $= 1 + i$
	Commented by mathdanisur last updated on 03/Aug/21

	$S e r, T h a n k Y o u$
	Answered by Ar Brandon last updated on 03/Aug/21

	$= \sqrt{2} \cdot \frac{e^{i 85 °}}{e^{i 40 °}} = \sqrt{2} e^{i 85 ° - i 40 °} = \sqrt{2} e^{i 45 °}$ $= \sqrt{2} (\cos 45 ° + i \sin 45 °) = 1 + i$
	Commented by mathdanisur last updated on 03/Aug/21

	$S e r, T h a n k Y o u$
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