Question

The product of (3 + 2i) and a complex number is (17 + 7i) im confused can some one explain what i do i dont know werither to divide them or multipy them

Answer 1

@shamim

Answer 2

Do u know
i=√(-1)

Answer 3

i^2=-1

Answer 4

yes

Answer 5

i know ths i^2 is just -1

Answer 6

so i get 37+45i

Answer 7

thank you hopefully its right this is my second time taking this quiz

Answer 8

U r most welcome!!!!

Answer 9

Anyway which grade u r studying?

Answer 10

12 grade liberal arts 2 and algebra 2

Answer 11

Let's call our unknown complex number z,
So we're told that (3+2i) times this complex number z, is equal to 17+7i,\[\large\rm (3+2i)z=17+7i\]To solve for z, we'll have to apply division,\[\large\rm z=\frac{17+7i}{3+2i}\]From there we will apply steps to put it into standard a+bi form.

I hope those steps make sense, yes?

Answer 12

so i used 3+2i as a conjugates right

Answer 13

z=17+7i/3=2i * (3-2i)/(3-2i) right

Answer 14

Multiplying by conjugate of your denominator?
Yes good.

So notice that the `numerator` that you end up with is the work that you already did! So that's good, we can use that for our numerator.

Answer 15

Woops woops woops :)
Nevermind, Our numerator is (17+7i)(3-2i) not (17+7i)(3+2i) like we had before. My mistake hehe

Answer 16

im confused now...

Answer 17

Sorry i was wrong to understand the meaning of ur math

Answer 18

\[\large\rm z=\frac{17+7i}{3+2i}\left(\frac{3-2i}{3-2i}\right)\]So we'll have some multiplication on the top and the bottom,
\[\large\rm z=\frac{(17+7i)(3-2i)}{(3+2i)(3-2i)}\]

Answer 19

On the bottom,
do you remember what happens when you multiply complex conjugates? :)

Answer 20

i foil them right

Answer 21

I think u know
a^2-b^2=(a+b)(a-b)

Answer 22

so i get 37/10 +45/10 i right

Answer 23

So
(3+2i)(3-2i)=3^2-(2i)^2=?

Answer 24

You `could` foil them, yes :)
But it's good to remember how conjugates work.

With real numbers, when you multiply conjugates,
you end up with `the difference of squares`.
Example: \(\large\rm (5-3)(5+3)=5^2-3^2=25-9\)

With complex numbers, when you multiply conjugates,
you end up with `the sum of squares`.
Example: \(\large\rm (5-3i)(5+3i)=5^2+3^2=25+9\)

Answer 25

okay im just going to move on im too confused .. but thank you

Answer 26

I can make it clearer if u give me time

Answer 27

its okay i can miss a question i just need 4 out of 5

Answer 28

Can u tell me
(2i)^2=?

Answer 29

-4?

Answer 30

3^2-(2i)^2=?

Answer 31

(17+7i)(3-2i)=?

Answer 32

U know
3^2-(2i)^2=13
Right?

Answer 33

13 and 65+7i

Answer 34

(17+7i)(3-2i)
=51+14+21i-34i
=65-13i

Answer 35

okay

Answer 36

(65-13i)/13=?
Right?

Answer 37

7/13 i

Answer 38

No

Answer 39

65/13-i