Question

Simplify the expression.

Answer 1

\[\frac{ \sqrt{-25} }{ (5-2i)+(1-4i) } \]

Answer 2

Choices:
\[\frac{ -5+15i }{ 16 }\]
\[\frac{ -5+5i }{ 12 }\]
\[\frac{ -1+3i }{ 4 }\]
\[\frac{ 5-5i }{ 12 }\]

Answer 3

You want the answer?

Answer 4

if someone could help explain the answer i would like that but the answer itself is fine i guess

Answer 5

Complex numbers can be added like any other numbers. So we can simplify the denominator that way. The numerator can also be simplified; we can factor out the "-1" from the square root and write it as sqrt(25)*sqrt(-1) = 5i. And that is the simplest it gets. This is how it will turn out to be:\[=\frac{ \sqrt{(-1)(25)} }{5-2i+1-4i }=\frac{ \sqrt{-1}\sqrt{25} }{ 6-6i }=\frac{ 5i }{ 6-6i }\] And that's the simplest it gets.

@touseii45

Answer 6

oh okay i did it wrong and got confused! thanks @genius12 for clearing that up for me(:

Answer 7

So the answer is\[\frac{ 5-5i }{ 12 } \]

Answer 8

or no its \[\frac{ -5+5i }{ 12 }\]