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 ~