Question

The equation is:
(sqrt[2]/2-sqrt[2]/2i)+(-sqrt[2]/2-sqrt[2]/2i)

Sorry if that's hard to understand. x_x
The i represents an imaginary number.
It's easier if you write the equation down on paper, probably.

Answer 1

\[(\frac{\sqrt2}{2}-\frac{\sqrt2}{2}i)+(-\frac{\sqrt2}{2}-\frac{\sqrt2}{2}i)\]?

Answer 2

Exactly!

Answer 3

This is not an equation.

Answer 4

Do you mean to simplify it?

Answer 5

What would it be considered?

Answer 6

Yes. Sorry about the confusion.

Answer 7

\[(\frac{\sqrt2}{2}-\frac{\sqrt2}{2}i)+(-\frac{\sqrt2}{2}-\frac{\sqrt2}{2}i)\]\[=\frac{\sqrt2}{2}-\frac{\sqrt2}{2}i-\frac{\sqrt2}{2}-\frac{\sqrt2}{2}i\]\[=\frac{\sqrt2}{2}-\frac{\sqrt2}{2}-\frac{\sqrt2}{2}i-\frac{\sqrt2}{2}i\]So, do the subtraction for the first two terms first, can you?

Answer 8

Would it be 0?

Answer 9

Yes!
So, you get \[=0-\frac{\sqrt2}{2}i-\frac{\sqrt2}{2}i\]Can you simplify the last two terms now?

Answer 10

Wouldn't that be 0? Or am I doing something wrong?

Answer 11

No
What is -a -a?

Answer 12

a?

Answer 13

No :S
What is -1 -1?

Answer 14

-2

Answer 15

Yup :)
What is -2 - 2?

Answer 16

-4!

Answer 17

Yup! So what is -100 -100?

Answer 18

-200.

Answer 19

Yup, so what is -a -a ?

Answer 20

-a?

Answer 21

No :S
-1 - 1 = - (1+1) = -2
-2 - 2 = - (2+2) = -4
-100 - 100 = - (100 + 100) = -200
-a - a = ...?

Answer 22

-a - a
-a + -a
right?

Answer 23

Yes. Which is?

Answer 24

is a+a=2a?

Answer 25

Yes
What is -a - a?

Answer 26

-2a?

Answer 27

Yes!

Answer 28

Now, remember we've got\[=0-\frac{\sqrt2}{2}i-\frac{\sqrt2}{2}i\]
We treated \(\frac{\sqrt2}{2}i\) = a, so it becomes
= 0-a -a
= ...?

Answer 29

0-2a? Which would be, -2a. right?

Answer 30

Yes!

Answer 31

Now, put back a = \(\frac{\sqrt2}{2}i\) into -2a, what do you get?

Answer 32

I think I'm having trouble with the square roots. How do I simplify them?

Answer 33

\[=-2 \times \frac{\sqrt2}{2}i = -\frac{2\sqrt2}{2}i\]There is something that you can cancel.

Answer 34

The 2's?

Answer 35

That aren't under the square root.

Answer 36

Yes :) What do you get then?

Answer 37

\[\sqrt{2}\]i

Answer 38

It's supposed to be next to the 2.

Answer 39

\[\sqrt2i\]Yes!

Answer 40

but with a negative sign!

Answer 41

\[=-2 \times \frac{\sqrt2}{2}i = -\frac{2\sqrt2}{2}i=-\frac{\cancel{2}\sqrt2}{\cancel{2}}i=-\sqrt2i\]