Question

simplify the expression (root-1)/(2-4i)-(5+3i)

Answer 1

answer choices are:

Answer 2

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

Answer 3

@Hero

Answer 4

@doulikepiecauseidont has it right. Simplify the denominator now.

Answer 5

how do i simplify it if there are negative numbers on the bottom?

Answer 6

(2 - 4i) - (5 + 3i)

Remember `-(5 + 3i)` = `-1(5 + 3i)` = -5 - 3i

Answer 7

how can that be the same thing if one sign is the same and the other is opposite?

Answer 8

Then you will have 2 - 4i - 5 - 3i

When you re-arrange it by placing like terms together you have

2 - 5 - 4i - 3i

Afterwards, you can re-group things again:

(2 - 5) - (4 + 3)i

or

- ( 5 - 2) - (4 + 3)i = -3 -7i

Answer 9

is -3-7i the same as -7-3i?

Answer 10

NO

Answer 11

is it the same as 3+7i?

Answer 12

no

Answer 13

Basically, this just means you have no clue what to do next to simplify this:

\[\frac{i}{-3 - 7i}\]

Answer 14

this is a valid statement

Answer 15

You can simplify it further to get
\[-\frac{i}{3 + 7i}\]

Answer 16

But you have to multiply top and bottom by the conjugate in order to continue simplifying.

Answer 17

so I would then multiply the top and bottom by (3-7i)

Answer 18

Yes. Make sure you do so carefully.

Answer 19

so the top would be 3i-7i^2
and the bottom would be 9+49i^2 ?

Answer 20

The bottom will be a difference of squares. But you don't do it like that.

Answer 21

so I don't foil and cancel the middle?

Answer 22

\[-\frac{i(3-7i)}{(3 + 7i)(3 - 7i)}\]

If you did it correctly, you'd get one of your answer choices.

Answer 23

\[i^2=-1\]

Answer 24

okay the top is 3i*-7i^2
which simplifies to 3i+7, yes?

Answer 25

Yes, but don't forget about the negative in front of the fraction

Answer 26

You have to distribute it across the numerator expression

Answer 27

which means that the numerator is really -3i+7?

Answer 28

No, not both

Answer 29

You don't know how to distribute a negative?

-(3i + 7) = ?

Answer 30

sorry, typo, meant to say -3i-7

Answer 31

What about the bottom? You should have gotten: \(9 - 49i^2\).

Answer 32

And after replacing \(i^2\) with -1, you should have \(9 - 49(-1))\)

Answer 33

ooooooh, revelation. I got it now, thanks soo much, both of you!

Answer 34

Just to confirm, what is the final result?

Answer 35

(-7-3i)/58

Answer 36

@Hero do you know anytihng about bearings?

Answer 37

I know about bearings

Answer 38

can you help me with my question, it says the play is travelling on a bearing of 340 degrees at 325 mph, doesn't that mean they are in QII not QIV?

Answer 39

the plane*

Answer 40

@Hero

Answer 41

Negative. You need to brush up on your quadrants. The plane is traveling in the 4th Quadrant.

Answer 42

I dont get it

Answer 43

isn't that a bearing of 340 degrees(20 degrees from the north line)