Question

Simplify the expression

Answer 1

\[\frac{ \sqrt{-4} }{ (5 + 2i) - (3 - 4i) }\]

Answer 2

Do you know what the numerator is, in terms of \(i\)?

Answer 3

2i?

Answer 4

3\10 + i 1\10

Answer 5

That's right. How about the denominator? What would you do to simplify it?

Answer 6

distributive property?

Answer 7

5 + 2i - 3 + 4i?

Answer 8

2 + 6i?

Answer 9

Yes, kudos!

Answer 10

yaay!!

Answer 11

then how do you go from here?

Answer 12

The numerator is \(2i\) and the denominator is \(2 + 6i \). Can you factor the denominator?

Answer 13

It will help us do some cancellations.

Answer 14

i give the answer [\frac{ 3 }{ 10 } + \frac{ i }{ 10 }]

Answer 15

factor in what way?

Answer 16

Like \(2 + 6i = 2(1 + 3i)\)

Answer 17

oohhh....okay...now what?

Answer 18

The numerator is \(\color{blue}2i\) and the denominator is \(\color{blue}2(1+3i)\). That bit of color will give a hint to you!

Answer 19

so those two cancel each other out!

Answer 20

Yeah, the 2s do, at least!

Answer 21

so whats the answer?

Answer 22

We're soon gonna find it. Right now, we have\[\dfrac{i}{i + 3i}\]

Answer 23

can the i's cancel out?

Answer 24

Not really, no.

Answer 25

oh wait a minute...these are the answers given on my assignment....

a. the quantity of three plus I all over ten
b. the quantity of three minus I all over ten
c. the quantity of three plus I all over eight
d. the quantity of three minus I all over eight

Answer 26

So your assignment hates when you put that \(i\) in the denominator. Do you know of a way to remove it from the denominator and get it to the numerator?

Answer 27

idk