Find the conjugate of each of the following:
(2 – 5i)2
Given: z = (2 – 5i)2
First we calculate (2 – 5i)2 and then we find the conjugate
(2 – 5i)2 = (2)2 + (5i)2 – 2(2)(5i)
= 4 + 25i2 – 20i
= 4 + 25(-1) – 20i [∵ i2 = -1]
= 4 – 25 – 20i
= -21 – 20i
Now, we have to find the conjugate of (-21 – 20i)
So, the conjugate of (- 21 – 20i) is (-21 + 20i)