Question:
Find the conjugate of each of the following:
$(2-5 i)^{2}$
Solution:
Given: $z=(2-5 i)^{2}$
First we calculate $(2-5 \mathrm{i})^{2}$ and then we find the conjugate
$(2-5 i)^{2}=(2)^{2}+(5 i)^{2}-2(2)(5 i)$
$=4+25 i^{2}-20 i$
$=4+25(-1)-20 i\left[\because i^{2}=-1\right]$
$=4-25-20 i$
$=-21-20 i$
Now, we have to find the conjugate of $(-21-20 \mathrm{i})$
So, the conjugate of $(-21-20 \mathrm{i})$ is $(-21+20 \mathrm{i})$
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