Question B.3: If A = 2+j5, B = 4−j6, find: (a) A^∗ (A+B), (b) (A+B)/(A−B).

(a) If A = 2 + j5, then A^{*} = 2 − j5 and
A + B = (2 + 4) + j(5 − 6) = 6 − j
so that
A^{*}(A + B) = (2 − j5)(6 − j) = 12 − j2 − j30 − 5 = 7 − j32

(b) Similarly,
A − B = (2 − 4) + j(5 − −6) = −2 + j11
Hence,

\frac{A+B}{A-B}=\frac{6-j}{-2+j 11}=\frac{(6-j)(-2-j 11)}{(-2+j 11)(-2-j 11)}
=\frac{-12-j 66+j 2-11}{(-2)^{2}+11^{2}}=\frac{-23-j 64}{125}=-0.184-j 0.512