Q. 2 C5.0( 4 Votes )

Simplify each of the following and express it in the form (a + ib) :

(–3 + 5i)3

Answer :

Given: (-3 + 5i)3

We know that,


(-a + b)3 = - a3 + 3a2b – 3ab2 + b3 …(i)


So, on replacing a by 3 and b by 5i in eq. (i), we get


-(3)3 + 3(3)2(5i) – 3(3)(5i)2 + (5i)3


= -27 + 3(9)(5i) – 3(3)(25i2) + 125i3


= -27 + 135i – 225i2 + 125i3


= -27 + 135i – 225 × (-1) + 125i × i2


= -27 + 135i + 225 – 125i [ i2 = -1]


= 198 + 10i



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