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 April 21st, 2011, 11:40 AM #1 Newbie   Joined: Apr 2011 Posts: 1 Thanks: 0 complex number to exponential form hello friends please help me... express this complex number to exponential form -2+j2
 April 21st, 2011, 12:35 PM #2 Math Team   Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus Re: complex number to exponential form $-2+2i=2(-1+i)=\frac{4}{\sqrt{2}}\left(-\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i\right)=\fra c{4}{\sqrt{2}}e^{\frac{3\pi}{4}i}$
 April 21st, 2011, 03:38 PM #3 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs Re: complex number to exponential form What ZardoZ did was utilize Euler's formula: $e^{ix}=\cos x+i\,\sin x$ $-2+2i=2$$-1+i$$=2\sqrt{2}$$\frac{-1+i}{\sqrt{2}}$$$ $\frac{-1+i}{\sqrt{2}}=\cos x+i\,\sin x$ thus: (1) $\cos x=-\frac{1}{\sqrt{2}}$ (2) $\sin x=\frac{1}{\sqrt{2}}$ Dividing (2) by (1) we get: $\tan x=-1\:\therefore\=\frac{3\pi}{4}" /> putting it all together, we have: $2\sqrt{2}e^{\frac{3\pi}{4}i}=2\sqrt{2}$$\cos\(\fra c{3\pi}{4}$$+i\,\sin$$\frac{3\pi}{4}$$\)=2\sqrt{2} $$\frac{-1+i}{\sqrt{2}}$$=-2+2i$
 April 21st, 2011, 04:12 PM #4 Math Team   Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus Re: complex number to exponential form [color=#000000]Analytical as always Mark [/color]

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### complex number in polar exponential in -i

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