Question

Express your answer in simplest a+ bi form. (8+5i)(3+2i)-(4+i)(4-i)

Answer 1

$\qquad\qquad\huge\underline{{\sf Answer}}$

Let's solve ~

$\qquad \sf \dashrightarrow \:(8 + 5i)(3 + 2i) - (4 + i)(4 - i)$

$\qquad \sf \dashrightarrow \:[( 8 \sdot3) + (8 \sdot2i) + (5i \sdot3) + (5i \sdot2i)] -[( 4 \sdot4) + (4 \sdot - i) + (i \sdot4) + (i \sdot - i)]$

$\qquad \sf \dashrightarrow \:[24+ 16i + 15i+ 10i {}^{2} ] -[16 - 4 i+ 4i - i {}^{2} ]$

$\qquad \sf \dashrightarrow \:[24+ 31i+ 10 {}{( - 1)} ] -[16 - ( - 1){}^{} ]$

$\qquad \sf \dashrightarrow \:[24+ 31i - 10 {}{} ] -[16 + 1{}^{} ]$

$\qquad \sf \dashrightarrow \:[14+ 31i {}{} ] -[17{}^{} ]$

$\qquad \sf \dashrightarrow \: - 3+ 31i {}{}$

I hope you understood the procedure ~