Question

if z=3-2i and w=-3+i evaluate 2z +3w​

Answer 1

Answer:

(i) z = 5 – 2i, w = -1 + 3i z + w = (5 – 2i) + (-1 + 3i) = (5 – 1) + (-2i + 3i) = 4 + i (ii) z – iw = (5 – 2i) – i (-1 + 3i) = 5 – 2i + i + 3 = (5 + 3) + (-2i + i) = 8 – i (iii) 2z + 3w = 2(5 – 2i) + 3 (-1 +3i) = 10 – 4i – 3 + 9i = 7 + 5 i (iv) zw = (5 – 2i) (-1 + 3i) = -5 + 15i + 2i – 6i = -5 + 17i + 6 = 1 + 17i (v) z2 + 2zw + w2 = (z + w)2 [from (i)] = (4 + i)2 = 16 – 1 + 8i = 15 + 8i (vi) (z + w)2 = 15 + 8z