Question

Multiply and simplify: (1 + 5i)(3 - 8i)

Answer 1

43 + 7i

Explanation:

Given: (1 + 5i)(3 - 8i)

To find: Multiplication and simplification

Solution:

i=
`√(-1)`,

Now, we simply open the brackets as follows:

(1 + 5i)(3 - 8i)

1(3 - 8i) + 5i (3 - 8i)

3 - 8i + 15i - 40
`i^(2)`

3 + 7i - 40
`i^(2)` - (i)


`i^(2)` = i * i


`i^(2)` =
`√(-1)` *
`√(-1)`


`i^(2)` = -1

Now, put
`i^(2)` = -1 into the equation (i)

we get

⇒ 3 + 7i -40(-1)

⇒ 3 + 7i + 40

⇒ 43 + 7i

∴ Final Answer : 43 + 7i

Answer 2

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

Here we go ~

what we need to know here is that :

`\qquad \sf  \dashrightarrow \:i \cdot i = - 1`

Now, let's proceed accordingly ~

`\qquad \sf  \dashrightarrow \:(1 + 5i) \cdot(3 - 8i)`

`\qquad \sf  \dashrightarrow \:(1 \cdot3) - (1 \sdot8i) + (5i \cdot3) - (5i \cdot8i)`

`\qquad \sf  \dashrightarrow \:3 - 8i + 15i - ( - 1)(40)`

`\qquad \sf  \dashrightarrow \:3 + 7i - ( - 40)`

`\qquad \sf  \dashrightarrow \:3 + 40 + 7i`

`\qquad \sf  \dashrightarrow \:43 + 7i`