Question

Which expression is equivalent to (4 + 7i)(3 + 4i)? –16 + 37i 12 – 28i 16 – 37i 37 + 16i

Answer 1

Choice A is correct answer.

Explanation:

Given expression is :

(4+7i)(3+4i)

We have to find the product of two binomials.

Multiplying each term of first binomial to each term of second binomial,we get

4(3+4i)+7i(3+4i)

4(3)+4(4i)+7i(3)+7(4i)

12+16i+21i+27i²

Using the definition of i, i² = -1

12+16i+21i +27 (-1)

12+16i+21i-28

Gathering like terms,we get

12-28+16i+21i

Adding like terms, we get

-16+37i Which is the answer.

Answer 2

The equivalent expression is
`\Rightarrow -16+37i`

A is correct

Explanation:

We are given two complex number and need to multiply it. To find equivalent fraction.

`(4+7i)(3+4i)`

Using Binomial product property: (a+b)(c+d)=ab+ad+bc+bd

`\Rightarrow (4+7i)(3+4i)`

`\Rightarrow 4(3)+4(4i)+7i(3)+7i(4i)`

`\Rightarrow 12+16i+21i+28i^2`

Combine the like term and simplify

`\Rightarrow 12-28+37i`
`\because \ \ i^2=-1`

`\Rightarrow -16+37i`

Hence, The equivalent expression is
`\Rightarrow -16+37i`