Question

simplify: 8/2+2i

Answer 1

is this \[\frac{8}{2+2i}\]

Answer 2

yes :)

Answer 3

so first, learn to write it correctly. if you are dividing by a sum, enclose it in parentheses...

8/(2+2i) is the correct way or as i did it in equation editor.

now, to solve, multiply the top and bottom by the conjugate of the denominator.

Answer 4

i would divide the top and bottom from 2+2i & i will get 16+16i / 4+12i^3?

Answer 5

no, multiply top and bottom by the conjugate of the denominator.

the denominator is 2+2i, right? so what is its conjugate?

Answer 6

isnt it the same?

Answer 7

http://www.mathwords.com/c/complex_conjugate.htm

http://www.mathsisfun.com/algebra/conjugate.html

have a look...

Answer 8

so the copnjugate would be 2-2i?

Answer 9

yes it is!

Answer 10

so now i just multiply it by the top and bottom?

Answer 11

you got it! tell me what you get.

Answer 12

16-16i/ 4-4i

Answer 13

nope.
\[\frac{ 8 }{2+2i }=\frac{ 8 }{2+2i }\cdot\frac{ 2-2i }{2-2i }=\frac{ 16-16i }{4-4i+4i-4i^2 }=\frac{ 16-16i }{4-4i^2 }\]

and \(i^2 = -1\), right? so put that in and see what you get.

Answer 14

16-16i/ 4+4
= 16-16i/ 8

Answer 15

yes and then simplify

Answer 16

and again, use the parentheses... it should be (16-16i)/8

Answer 17

4-4i/ 2

Answer 18

parentheses? and is it completely simplified?

Answer 19

(2-2i)/1