Question

perform the indicated operation. write the answer in the form a +
(2 - 5i)^2 = □

Explanation:

Step1: Expand using formula $(a - b)^2=a^2-2ab + b^2$

Here $a = 2$ and $b = 5i$, so $(2-5i)^2=2^2-2\times2\times5i+(5i)^2$.

Step2: Calculate each term

$2^2 = 4$, $2\times2\times5i=20i$, and $(5i)^2=25i^2$. Since $i^2=- 1$, then $(5i)^2=25\times(-1)=-25$.

Step3: Combine the terms

$4-20i - 25=-21-20i$.

Answer:

$-21 - 20i$