4) Express the following in the form of a+ib,
a, beRi= V-1. State the values of a and b.
(1+i)^-3
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Answer:
(1+i)^-3
= 1/(1+i)^3
= 1/(1+i)(1+i)(1+i)
= 1/(1+i^2+2i)(1+i)
= 1/(1-1+2i)(1+i)
= 1/2i(1+i)
= 1/2(i+i^2)
= 1/2(i-1)
Rationalization
= 0.5(i+1)/(i^2-1)
= 0.5(i+1)/(-1-1)
= -0.25(i+1)
= -0.25 - 0.25i
Compared to a+bi
a = - 0.25
b = - 0.25
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