(1) We have:
x3 + iy3 = - 4 – i
and: arg(z3) = arctan(y3/x3) = arctan(-1/-4) = arctan(0.25)
so q = arg(z3) = 14 deg.
The value of r3= [x32 + y32]1/2 = [(-4)2 + (-1)2]1/2 = [17]1/2 = 4.1
So: z3 = 4.1 cos(14) + isin(14) = 4.1 cis(14)
(2) Recall: C = z4 = 4 + 3i
Thence: z5 = [z3 + z4] = [(-4 – i) + (4 – 3i)] = 0 – 4i
arg(z5) = arctan(y5/x5) = arctan(4 /0) = ¥
(No polar form applicable for an infinity) Cont'd
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