Question

[4pts] Consider the following four complex numbers A 3-j2 C-6 exp(-1144°) D -5 exp(j64°) and use them throughout this question. a. Translate each complex number into the form indicated: exp(j exp(j b. Determine the value of each complex number below and enter your answer using the form indicated: exp(j exp (You should enter at least 4 digits of precision. Your answer must be within 0.05% to be marked correct.)

Answer 1

Let A = 3 - 2j since, complex number a notequal bj to exponential form is r exp(theta j) where r = squareroot a^2 + b^2 & theta = tan^-1(b/a) therefore Here, a = 3, b = -2 r = squareroot (3)^2 + (-2)^2 = squareroot 9 + 4 = squareroot 13 = 3.6055 therefore theta = tan^-1(- 2/3) = tan^-1(0.6666) = 33.6874 degree therefore A = 3.6055 exp (j 33.6874 degree) Let B = -4 + j8 therefore r = squareroot (- 4)^2 + (8)^2 = squareroot 16 + 64 = squareroot 80 = 8.9442 theta = tan^-1(8/- 4) = tan^-1(- 2) = -63.4339 degree therefore B = 8.9442 exp(j - 63.4349 degree) Let c = 6 exp(- j 144 degree) therefore r = 6, theta = -144 degree therefore 6 = squareroot a^2 + b^2 rightarrow 36 = a^2 + b^2 - (1) - 144 = tan^-1 (b/a) rightarrow tan(-144) = b/a rightarrow 0.7265