1) use Euler\'s formula to rewrite e^(i2(theta)) 2) use e^(i2(theta)) = (e^(i(th

Question

1) use Euler's formula to rewrite e^(i2(theta)) 2) use e^(i2(theta)) = (e^(i(theta))^2 to rewrite e^(i2(theta)) in the form a + bi 3) set these answers to parts a and b (1,2) equal together to derive two famous trig identities 4) use substitution to evaluate integral of e^((a+bi)x) dx. Rewrite your answer using Euler's formula 5) Rewrite integral of e^((a+bi)x) dx as the sum of 2 integrals using algebra. hint: e((a+bi)x) = e^(ax) * e^(bxi) 6) set you answers to parts a and b equal to each other (4,5) by using known integral tables please help me! and show me the steps:)

Explanation / Answer

e^i2 =cos2+isin2

b)(cos+isin)^2= cos^2-sin^2+2isincos= cos^2-sin^2+i2sincos

c)eqauting above cos2+isin2= cos^2-sin^2+i2sincos

eqauting real and imaginary part

cos2=   cos^2-sin^2

son2= 2sincos

d)e^((a+bi)x) dx a+bi)x =t==>dt= bidx==>dx= 1/bi *dt

1/bie^(t)dt= 1/bie^(t)

e)e^((a+bi)x) dx= e^ax+ e^ibx= e^ax+ cosbx+isinbx

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