Q2 of 202 Page 171

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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