Simplify each of the following and express it in the form (a + ib) :
Given: (2 - √-3)2
We know that,
(a – b)2 = a2 + b2 – 2ab …(i)
So, on replacing a by 2 and b by √-3 in eq. (i), we get
(2)2 + (√-3)2 – 2(2)(√-3)
= 4 + (-3) – 4√-3
= 4 – 3 – 4√-3
= 1 – 4√3i2 [∵ i2 = -1]
= 1 – 4i√3
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