Question

Simplify 4 over -2 - 2i

-1 - i
-2 - i
-1 + i
-2 + i

Answer 1

\[\huge\rm \frac{ 4 }{ -2-2i }\]
multiply top and bottom of the fraction by the conjugate of the denominator

Answer 2

what does that mean?

Answer 3

do you know what conjugate is ?

Answer 4

no

Answer 5

conjugate of a +bi is `a-bi` change the sign of imaginary term

Answer 6

so what's the conjugate of `-2-2i` ?

Answer 7

-2+2i?

Answer 8

right now multiply numerator and denominator by `-2+2i`\[\large\rm \frac{ 4 }{ -2-2i }*\frac{-2+2i}{-2+2i}\]

Answer 9

familiar with the distributive property ?

Answer 10

lol dude basically you flip the middle sign of the denometer and multiply its by the numerator

Answer 11

multiply by both *denominator and numerator *

Answer 12

I still dont understand.

Answer 13

it's like rationalize the denominator when we have to move radical sign from bottom to the top

Answer 14

to move the imaginary term from the denominator we should multiply top and bottom by the `conjugate ` of the denominator (which is -2-2i)

Answer 15

conjugate of -2-2i is `-2+2i` right so now multiply both top and bottom by -2+2i make sense ?

Answer 16

so... 4 and -2+2i times -2+2i?

Answer 17

right \[\large\rm \frac{ 4 }{ -2-2i }*\frac{-2+2i}{-2+2i}\]
which can be written as \[\large\rm \frac{ 4(-2+2i) }{ (-2-2i)(-2+2i) }\]

Answer 18

then what?

Answer 19

now apply distributive property 4(-2+2i)
and foil (-2-2i)(-2+2i)

Answer 20

so -8+8i over 4 - 2i ?

Answer 21

distributive property \[\rm a(b+c)=a*b+a*c=ab+ac\]

Answer 22

-8+8i is correct
but how did you get 4-2i ?

Answer 23

remember \[\large\rm i= \sqrt{-1} ~~~and ~~~~~~~~~i^2= -1\]

Answer 24

I don't understand the bottom part I tried foil but I don't get it and I need to finish this test

Answer 25

how did you foil it. show your work . i'll try to find out the mistake