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Find the real and imaginary part of sin(4+3i) 
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#1
Sep1810, 05:21 PM

P: 70

1. The problem statement, all variables and given/known data
Find the real and imaginary part of sin(4+3i) 2. Relevant equations sinx = [tex]\frac{e^z  e^(z)}{2i}[/tex] cosx = [tex]\frac{e^z + e^(z)}{2}[/tex] sin(iy) = i[tex]\frac{e^y  e^(y)}{2}[/tex] cos(iy) = [tex]\frac{e^y + e^(y)}{2}[/tex] various trig identities 3. The attempt at a solution So I used sin(x+y) trig identity and got sin4*cos3i + sin3i*cos4 I turned them all into exponents using the appropriate equations stated in (2). I got to a point where nothing is really calculable by hand/head. Is there an easier way to do this or does the calculator need to be used at a certain point to calculate the real part(terms grouped w/o i) and the imaginary part (terms grouped with i). If so, then I guess I need help getting the terms grouped together to calculate the real and imaginary parts. Where I am stuck is at: [tex]\frac{e^{3+4i}+e^{3+4i}e^{34i}+e^{34i}}{4i}[/tex] + [tex]\frac{e^{3+4i}e^{3+4i}+e^{34i}e^{34i}}{4}[/tex] (the two fractions should be added together) Now what should I do with all these lovely exponents? Should I have even gone this route? 


#2
Sep1810, 06:13 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,553




#3
Sep1810, 06:46 PM

P: 70

That was just the hint I needed, Halls. Thanks! Finally got it.



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