Question

Find the product of (x + 9i)^2
Find the product of (x+(3+5i))^2

Answer 1

remember that
$i = \sqrt{1}$
so
${i}^{2} = - 1 \: \: and \: \: {i}^{3} = - i \: \: \: and \: \: {i}^{4} = 1$
(a+ b)^2 = a^2 + 2ab + b^2

1. x^2 + 2x*9i + (9i)^2 = x^2 + 18xi - 81

2. x^2 + 2x*(3+5i)+ (3+5i)^2 = x^2 + 6x + 10xi+ 9+30i-25 = x^2 - 16 + 30i + 6x + 10xi