Question

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

Answer 1

ANSWER

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

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: $64+47i$

Step-by-step 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:

$i=\sqrt{-1}\\\\i^2=-1$

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

 $28-16i+63i-36(-1)=28-16i+63i+36$

3. Finally, add the like terms:

$64+47i$