Question

Find inner product of the following vector:
<(1-i)/2, -(1+i)/2> and <(2+i)/3,-(2i)/3>

Answer 1

the inner product is the sum of the products of the corresponding components

\[\langle x_1,x_2,x_3\rangle\cdot\langle y_1,y_2,y_3\rangle=x_1y_1+x_2y_2+x_3y_3\]

Answer 2

HAHAH but How do I deal with the imaginary part?

Answer 3

just remember \(i^2=-1\)

Answer 4

can you show me where your geting stuck..?

Answer 5

sure... I am new to open study wait

Answer 6

I get this answer but it is incorrect.....

Answer 7

\[=\frac{ -3i^2-3i+2 }{ 6 }\]

Answer 8

what's your answer?

Answer 9

before your comment...

Answer 10

that is wrong according to Wolf
http://www.wolframalpha.com/input/?i=%7B%281-i%29%2F2%2C+-%281%2Bi%29%2F2%7D.+%7B%282%2Bi%29%2F3%2C-%282i%29%2F3%7D

Answer 11

\[\left\langle \frac{1-i}2, -\frac{1+i}2\right\rangle\cdot\left\langle \frac{2+i}3,-\frac{2i}3\right\rangle=\frac{1-i}2\frac{2+i}3+\frac{1+i}2\frac{2i}3\]

Answer 12

gotta go ..

Answer 13

\[=\frac{(1-i)(2+i)+(1+i)2i}6\]

Answer 14

Thank I try again...

Answer 15

by the way is -2i

Answer 16

both of the second terms were negative so their product is positive

Answer 17

the answer is pretty neat when you get to it

Answer 18

so the answer is \[\frac{ i+1}{ 6 }\] Rite?

Answer 19

\[\Large\color{red}\checkmark\]

Answer 20

How do I mark the question being solved?

Answer 21

in Open study

Answer 22

you could type this
```
\[\Large\color{red}\checkmark\]
```

Answer 23

\[\Large\color{red}\checkmark\]

Answer 24

cool

Answer 25

if you want to know what someone typed ,
right click (on some \(\LaTeX\); show math as;tex commands, and you can copy past it into
```
\[...\]
```
these brackets

Answer 26

you might want to check this space http://openstudy.com/study#/groups/LaTeX%20Practicing!%20%3A)