Question

Which of the following statements are true about the simplified form of the expression (2+2i)÷(1-i)? select all that apply

a) The simplified form is 2i **
b) the simplified form is 4i
c) the simplified form is 2+2i
d) the simplified form is 4+4i
e) the simplified form is a complex number because complex numbers are closed under division
f) the simplified form is not a complex number because complex numbers are not closed under division.

2 answers.

Answer 1

`(2+2i)/(1-i)=((2+2i)(1+i))/(1+1)=(2+2i+2i-2)/(2)=2i`

So, it's a) for sure. The other one is most likely e), but I'm not sure if it's true in general, that complex numbers are closed under division.

Answer 2

Option and e are correct.

Explanation:

Given Expression:

`(2+2i)/(1-i)`

We simplify the given expression to select the correct option.

Consider,

`(2+2i)/(1-i)`

`=(2+2i)/(1-i)*(1+i)/(1+i)`

`=((2+2i)(1+i))/((1-i)(1+i))`

`=(2-2+i(2+2))/((1)^2-(i)^2)`

`=(4i)/(1-(-1))`

`=(4i)/(2)`

`=2i`

2i is complex number.

Therefore, Option a and e are correct.