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Three vectors, A, B, and C, are related as follows: A/C = 2 at 120 deg, A + B = -5 + j15, C = conjugate of B. Find C.

Correct answer:

x =  11.9936
y =  2.8868

Step-by-step explanation:

A/C=2 ∠120 ∘ A+B = −5+15j C=conj B  W=2 ∠ 120°  = 2 ⋅ (cos 120° + j sin 120°)  = −1+1.7320508j W=(−1,1.7320508)  A=C ⋅  W A+ conj C = −5+j15​  −5+j15​ − conj C = C ⋅  W  j2 = −1 (a+bj)(c+dj) = (ac−bd) + (ad+bc)j  C = x+jy​ −5+j15​ − (x−jy​) = (x+jy​) ⋅  (−1+1.7320508j)  x=11.9936 y=2.88675≐2.8868
y==2.8868

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