Write the following in amplitude phase form, C*e i a.) 1+i= Solution e^(ix) = co
ID: 1818867 • Letter: W
Question
Write the following in amplitude phase form, C*ei
a.) 1+i=
Explanation / Answer
e^(ix) = cos(x) + i*sin(x) (a) cos(x) = sin(x) => x= 45 degrees. C=sqrt (2). 1+i = 2^.5 * (1/2^.5 + i / 2^.5) = 2^.5 * e^(i*45) = 1.414 * e^(i*45) (b) e^(-x) = 1/e^(x). hence 1/(1+i) = 1/2^.5 * e^(i*45) = (1/2^.5)*e^(i*-45) = .707 * e^(-45) (c)2-i =(2^2+1)*[ 2/(2^2+1) - i/(2^2+1)] = 5^.5 *[cos(26.565)+i*sin(26.565)]= 5^.5 * e^(i*26.565) = 2.236 * e^(i*26.565) 2-i/1+i =2.236* e^(i*26.565) * .707 * e^(i*-45) = 1.5808*e^(i*-18.435) (d) 3+4i = 5*e^(i*53.13) 1-2i = 2.236*e^(i*63.435) -2+i = -2.236 * e^(i*153.438) 1+i = 1.414 * e^(i*45) hence , (-2+i)/[(1-2i)*(3+4i)*(1+i)] = [-2.236/(2.236*5*1.414)] * e ^ [153.438 - 53.13-63.435-45] =-.14144 * e^(i*-8.127).
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