Question

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

Answer 1

Answer:

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

A is correct

Step-by-step 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 $\Rightarrow -16+37i$    

Answer 2

Answer:

Choice A is correct answer.

Step-by-step 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.