Question

Multiply and simplify: (2 + 6i)(8 – 9i)

Answer 1

Answer:
`70\text{ + 30i}`Step-by-step explanation:

Given:

`(2\text{ + 6i\rparen\lparen8 - 9i\rparen}`

To find:

To multiply and simplify

First, we will expand using distributive property:

`\begin{gathered} (2\text{ + 6i\rparen\lparen8 - 9i\rparen = 2\lparen8 - 9i\rparen + 6i \lparen8 - 9i\rparen} \\ \\ =\text{ 2\lparen8\rparen- 2\lparen9i\rparen+ 6i\lparen8\rparen+ 6i \lparen-9i\rparen} \end{gathered}`
`\begin{gathered} $$mu\text{ltiplication of same signs give positive sign}$$ \\ $$m\text{ ultiplication of opposite signs give negative sign}$$ \\ =\text{ 16 - 18i + 48i - 54i}^2 \\ \\ =\text{ 16 + 30i - 54i}^2 \\ \\ In\text{ complex numbers, i}^2\text{ = -1} \\ \\ =\text{ 16 + 30i - 54\lparen-1\rparen} \end{gathered}`
`\begin{gathered} =\text{ 16 + 30i + 54} \\ \\ =\text{ 70 + 30i} \end{gathered}`