Find the conjugate of each of the following : (2 – 5i)2

1.	Find the conjugate of each of the following : (2 – 5i)2
Answer» 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)

Answer»

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)

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