Simplify each of the following and express it in the form (a + ib) :
(5 – 2i)2
Given: (5 – 2i)2
We know that,
(a – b)2 = a2 + b2 – 2ab …(i)
So, on replacing a by 5 and b by 2i in eq. (i), we get
(5)2 + (2i)2 – 2(5)(2i)
= 25 + 4i2 – 20i
= 25 – 4 – 20i [∵ i2 = -1]
= 21 – 20i