Question

write in the form a+bi
(3-i)/(2-i) X (3+i)/(4+i)

Answer 1

do you know what "conjugate" is?

Answer 2

lol I wa about to tag you

Answer 3

;)

Answer 4

\(i^2=-1\)
And; \((a-b)(a+b)=a^2-b^2\)

(you need to know these)

Answer 5

yeah I know that you cant have complex numbers in the denominator and you have to multiply by the conjugate

Answer 6

that is awesome at start, I see so many people that don't know that....

Answer 7

\(\large\color{#000000 }{ \displaystyle \frac{(3-i)}{(2-i)} \times \frac{(3+i)}{(4+i)} }\)

via: \((a-b)(a+b)=a^2-b^2\)
and after expanding the bottom as well;

we get,
\(\large\color{#000000 }{ \displaystyle \frac{3^2-i^2}{8+2i-4i-i^2} }\)

Answer 8

\(\large\color{#000000 }{ \displaystyle \frac{3^2--1}{8+6i--1} }\)

\(\large\color{#000000 }{ \displaystyle \frac{9+1}{8+6i+1} }\)

\(\large\color{#000000 }{ \displaystyle \frac{10}{9+6i} }\)

Answer 9

now top and bottom times conjugae

Answer 10

(times 9-6i)

Answer 11

\(\large\color{#000000 }{ \displaystyle \frac{10(9-6i)}{(9+6i)(9-6i)} }\)

go for it :)

Answer 12

okay I think im doing it wrong but I get 90-60i/ 117

Answer 13

Why wrong?

\(\large\color{#000000 }{ \displaystyle \frac{10(9-6i)}{(9+6i)(9-6i)} }\)

\(\large\color{#000000 }{ \displaystyle \frac{90-60i}{81-36i^2} }\)

\(\large\color{#000000 }{ \displaystyle \frac{90-60i}{81-36(-1)} }\)

\(\large\color{#000000 }{ \displaystyle \frac{90-60i}{81+36} }\)

\(\large\color{#000000 }{ \displaystyle \frac{90-60i}{117} }\)

Answer 14

You are doing it correctly, good job !!

Answer 15

You just needed one step more to get it into an "a+bi" form

Answer 16

\(\large\color{#000000 }{ \displaystyle \frac{90}{117}+\frac{-60}{117}i }\)

Answer 17

1+1+7=9
Therefore 117 can be divided by 3.

Answer 18

So now, reduce the fractions

Answer 19

((This is another good rule, if the sum of digits of a number is divisible by 3, then the number itself is also divisible by 3....

And it is also true that if the sum of digits of a number is divisible by 9, then the number itself is divisible by 9... ))

Answer 20

the answer I get is not an answer choice...

Answer 21

the answer is 18/17+4/17i