Question

Simplify the expression: sqrt of -25/(5-2i)+(1-4i)

Answer 1

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

Answer 2

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

Answer 3

Whoops, forgot a plus sign in the second one.

Answer 4

Ok so would I multiply the numerator and denominator by 1-4i?

Answer 5

No no, sorry I was asking to clarify how to problem is written. :/

Answer 6

\[\frac{ \sqrt{-25} }{ 5-2i }+(1-4i)\]
That is what i meant to write.

Answer 7

Is it that one, or the first one i wrote?

Answer 8

the first one

Answer 9

Okay, that makes things a bit easier. The parentheses are meaningless here. You can easily simplify the denominator. We can also simplify the numerator. What do you think those would be?

Answer 10

5i is the numerator and 6-6i is the numerator?

Answer 11

sounds good to me.

Answer 12

Now I'm not sure how much more "simple" you need to take it. Usually you try to get rid of the complex number from the denominator like what you usually do if you have a radical in the denominator.

Answer 13

so do i multiply the numerator and denominator by the the conjugate of the denomiator?

Answer 14

To do this, you need to multiply it by it's complex conjugate. Have you heard about that before?

Answer 15

HAHA, that's great. We were on the same page and typing the same thing. Yes, that's exactly what you'd do.

Answer 16

yes

Answer 17

so how would I do that exaclty?

Answer 18

\[\frac{ 5i }{ 6-6i }*\frac{ 6+6i }{ 6+6i }\]
The \[\frac{ 6+6i }{ 6+6i }\] is how we multiply by the complex conjugate. You'll notice it's just a "fancy" way of multiplying by one. This is probably one of the most important "tricks" you do in math, along with adding "zero" in fancy ways.

Answer 19

What would the answer be? 30i+30i^2/72?

Answer 20

This is where i get lost?

Answer 21

which can be simplified. :D
Do you know what i^2 is?

Answer 22

also there are some common factors on top and bottom which can reduce everything.

Answer 23

i^2=-1

Answer 24

okay so what would my answer be?

Answer 25

I don't want to just give you the answer. You're 100% correct so far though. Lets put everything you have together though.
\[\frac{ 30i+(-30) }{ 72 } = \frac{ 30i-30 }{ 72 }\]

Now lets start with 2. Does 2 go into 30 and 72?

Answer 26

yes but wouldn't 6 be a better choice?

Answer 27

It could be, but I always start with the lowest term possible. 2 is always a safe bet and if 2 doesn't work, try 3....and so on.

Answer 28

is -5+5i/12 my answer?

Answer 29

Yup!