Question

Write the result of (4+9i)(7-4i) in a+bi form​

Answer 1

`(4 + 9i)(7 - 4i) = 64 + 47i`

EXPLANATION

The given complex number expression is:

`(4 + 9i)(7 - 4i)`

We expand using the distributive property to get;

`(4 + 9i)(7 - 4i) = 4(7 - 4i) + 9i(7 - 4i)`

`(4 + 9i)(7 - 4i) = 28- 16i + 63i - 36 {i}^(2)`

Recall that,

`{i}^(2) = - 1`

Our expression now simplifies to:

`(4 + 9i)(7 - 4i) = 28 + 47i + 36`

`(4 + 9i)(7 - 4i) = 64 + 47i`

Answer 2

Answer:
`64+47i`

Explanation:

Given the Complex numbers multiplication:

`(4+9i)(7-4i)`

You need to follow these steps:

1. Apply Distributive property:

`(4+9i)(7-4i)=(4)(7)+(4)(-4i)+(9i)(7)+(9i)(-4i)=28-16i+63i-36i^2`

2. You need to remember that:

`i=√(-1)\\\\i^2=-1`

Then, you need to substitute
`i^2=-1`:

`28-16i+63i-36(-1)=28-16i+63i+36`

3. Finally, add the like terms:

`64+47i`