Question

Simplify 3 over quantity of 5 minus 6 i

quantity of 15 plus 18 i over 61

quantity of negative 15 plus 18 i over 61

3 i over quantity of 6 plus 5 i

quantity of 15 plus 18 i over negative 11

Answer 1

"3 over quantity of 5 minus 6i" can be written as : \(\cfrac{3}{5-6i}\) , right?

Answer 2

correct.

Answer 3

Okay, so, in order to simplify this, we will multiply numerator and denominator by the conjugate of 5-6i

Can you tell me what is the conjugate of 5 - 6 i ?

Answer 4

(2 + i)(3 + 4i)?

Answer 5

@mathslover

Answer 6

@kiaracakes120513 what about the first question? it is not yet solved..

Answer 7

umm i have no clue..

Answer 8

Do you know about conjugate of "a + bi" ?

Answer 9

nope..

Answer 10

See, the conjugate of a+bi is a-bi

Answer 11

so, conjugate of 5 -6i is 5 + 6i

Answer 12

ohhh okay so it basically you just switch the sign

Answer 13

Right!

Answer 14

So, we will multiply 5 + 6i to numerator and denominator ...

\(\cfrac{3}{5-6i} \times \color{Blue}{\cfrac{5 + 6i}{5 + 6i} }\)

\(\cfrac{3(5+6i)}{(5-6i)(5+6i)}\)

Answer 15

Now we will use (a-b)(a+b) = a^2 - b^2 identity here for the denominator.

Answer 16

Can you simplify it further?

Answer 17

no..?

Answer 18

Okay, we will first simplify the denominator...

AS : \((a+b)(a-b) = a^2 - b^2 \)

So , (5+6i)(5-6i) = ?

Answer 19

61

Answer 20

Yep... good! So, denominator becomes 61

and numerator now..

Answer 21

3(5+6i) = 3(5) + 3(6i) = ?

Answer 22

it simplifies out to 0

Answer 23

@mathslover

Answer 24

No... 3(5) + 3(6i) = 15 + 18 i

Answer 25

Ohh

Answer 26

So, you get (15+18i)/61

Answer 27

yea

Answer 28

so thats the answer?

Answer 29

You need to convert this in statement now.

Answer 30

what does that mean? lol

Answer 31

Just like the question was written and we converted it into equations! So, you do vice versa..

Answer 32

ohh okayy