Question

ALGEBRA 2 QUESTION URGENT HELP PLEASE!!

Simplify the expression the root of negative sixteen all over the quantity of three minus three i plus the quantity of one minus two i.

ANSWER CHOICES
a. the quantity of negative twenty minus sixteen i all over nine.
b. the quantity of eight plus four i all over fifteen.
c. the quantity of eight minus four i all over fifteen.
d. the quantity of negative twenty plus sixteen i all over forty one.

Answer 1

–6

Explanation:

Answer 2

d. the quantity of negative twenty plus sixteen i all over forty one.

Explanation:

We want to simplify the complex number:

`(√(-16) )/((3-3i)+(1-2i))`

We rewrite to obtain:

`(√(16)* √(-1) )/((3+1)+(-3i-2i))`

Recall that:
`√(-1)=i` and
`-1=i^2`

We simplify to get:

`(4i)/(4-5i)`

We rationalize to get:

`(4i)/(4-5i)*(4+5i)/(4+5i)`

`(4i(4+5i))/((4-5i)(4+5i))`

`(16i+20i^2)/(4^2+5^2)`

`(16i-20)/(16+25)`

`(-20+16i)/(41)`

The correct answer is D