Question

Perform the indicated operation and write the answer in the form a + bi.
(3 +81) (4-3i)

Answer 1

SOLVING

`\Large\maltese\underline{\textsf{A. What is Asked \space}}`

Perform the indicated operation and write the answer with the form a+bi.

2 numbers given, one of which is complex

`\Large\maltese\underline{\textsf{B. This problem has been solved!\space\space}}`

Multiply these two numbers, just like you always multiply binomials.

`\bf{(3+8i)(4-3i)}` | multiply

`\bf{3*4+3*(-3i)+8i*4+8i*(-3i)}` | simplify

`\bf{12-9i+32i-24i^2}` | this can be simplified A LOT

`\bf{12+23i-24i^2}` | as strange as it may seem, this can be simplified even more, because isn't i^2 the same as -1?

`\bf{12+23i-24*(-1)}=12+23i+24}` | add 12 and 24

`\bf{36+23i}`

`\rule{300}{1.7}`

`\bf{Result:}`

`\bf{=36+23i}`. The answer is written in the form a+bi, as requested.

`\boxed{\bf{aesthetic\\ot101}}`

Answer 2

`\quad \huge \quad \quad \boxed{ \tt \:Answer }`

`\qquad \tt \rightarrow \: 36 + 23 i`

____________________________________

`\large \tt Solution \: :`

`\qquad \tt \rightarrow \: (3 + 8i)(4 - 3i)`

`\qquad \tt \rightarrow \: (3 \sdot 4)+ (3 \sdot - 3i) + (8i \sdot4) + (8i \sdot - 3i)`

`\qquad \tt \rightarrow \: 12 - 9i + 32i - (24 {i}^(2) )`

`\qquad \tt \rightarrow \: 12 + 23i -( 24 \sdot - 1)`

`\qquad \tt \rightarrow \: 12 + 23i + 24`

`\qquad \tt \rightarrow \: 36 + 23i`

Answered by : ❝ AǫᴜᴀWɪᴢ ❞