Question

(6+6i)/(7+6i)

Answer 1

Multiply top and bottom by 7-6i

Answer 2

7-6i is the conjugate of the denominator 7+6i

Answer 3

So what is (7+6i)(7-6i)

Answer 4

where are you getting "denominator" from Jim?

Answer 5

i just need to de divide the two....

Answer 6

not sure what you mean

Answer 7

Oh this is divide! I didn't see the divide sign!

Answer 8

Sorry Jim, you're in the right :P

Answer 9

So can you tell me what (7+6i)(7-6i) is alisson123?

Answer 10

She doesn't really understand it yet, this is her first time :/

Answer 11

no i can't..... i don't know what i;m doing....

Answer 12

i'm just trying to figure out the answer..... i'm taking a quiz and the teacher is no help

Answer 13

ok, let's FOIL it out

Answer 14

foil is for multiplication

Answer 15

(7+6i)(7-6i)

Multiply the First terms: 7*7 = 49

Multiply the Outer terms: 7*(-6i) = -42i

Multiply the Inner terms: 6i*(7) = 42i

Multiply the Last terms: 6i*(-6i) = -36i^2 = -36(-1) = 36

Now add up all the terms:


49+(-42i)+42i+36 = 85

Answer 16

So (7+6i)(7-6i) = 85

Answer 17

Now multiply out (6+6i)(7-6i)


(6+6i)(7-6i) = 6*7 + 6*(-6i) + 6i*(7) + 6i*(-6i)

(6+6i)(7-6i) = 42 - 36i + 42i - 36i^2

(6+6i)(7-6i) = 42 - 36i + 42i - 36(-1)

(6+6i)(7-6i) = 42 - 36i + 42i + 36

(6+6i)(7-6i) = 78 + 6i

Answer 18

So we go from

\[\Large \frac{6+6i}{7+6i}\]

to

\[\Large \frac{(6+6i)(7-6i)}{(7+6i)(7-6i)}\]

to

\[\Large \frac{78 + 6i}{85}\]

From there, break up the fraction to get

\[\Large \frac{78}{85} + \frac{6}{85}i\]

Answer 19

So in the end, \[\Large \frac{6+6i}{7+6i} = \frac{78}{85} + \frac{6}{85}i\]