Answer:
d. the quantity of negative twenty plus sixteen i all over forty one.
Step-by-step explanation:
We want to simplify the complex number:
[tex]\frac{\sqrt{-16} }{(3-3i)+(1-2i)}[/tex]
We rewrite to obtain:
[tex]\frac{\sqrt{16}\times \sqrt{-1} }{(3+1)+(-3i-2i)}[/tex]
Recall that: [tex]\sqrt{-1}=i[/tex] and [tex]-1=i^2[/tex]
We simplify to get:
[tex]\frac{4i}{4-5i}[/tex]
We rationalize to get:
[tex]\frac{4i}{4-5i}\times\frac{4+5i}{4+5i} [/tex]
[tex]\frac{4i(4+5i)}{(4-5i)(4+5i)}[/tex]
[tex]\frac{16i+20i^2}{4^2+5^2}[/tex]
[tex]\frac{16i-20}{16+25}[/tex]
[tex]\frac{-20+16i}{41}[/tex]
The correct answer is D
