Question

What is the value of the expression given below?

(5 + 3i) - (5 + 3i)(5 – 5i)
A. –5 + 371
B. 35 – 131
OC -5 – 371
D. –35 + 131

Answer 1

D -35+131

this is your answer

Answer 2

D. -35+13i

Explanation:

We have the expression
`(5+3i)-(5+3i)(5-5i)`, first we have to solve:

`(5+3i)(5-5i)` we have to apply distributive property.

Distributive property:
`(a+b)(c+d)=ac+ad+bc+bd`

Then,

`(5+3i)(5-5i)=5.(5)+5.(-5i)+3i.(5)+3i.(-5i)\\(5+3i)(5-5i)=25-25i+15i-15i^2\\(5+3i)(5-5i)=25-10i+15\\(5+3i)(5-5i)=(40-10i)`

Observation:
`i^2=(-1)` then
`-15i^2=-15.(-1)=15`

Now replacing
`(5+3i)(5-5i)=(40-10i)` in
`(5+3i)-(5+3i)(5-5i)`:

`(5+3i)-(40-10i)=5+3i-40+10i=(5-40)+(3i+10i)=-35+13i`

Then the correct answer ir: D. -35+13i