Question

4+2i / 1- 3i

Answer 1

@jay847 Do you know what's i ?

Answer 2

No it doesn't say

Answer 3

i is the square root of -1, it's a complex no.
\[\sqrt {-1}=i\]

Answer 4

Ok so u multiply it by -1

Answer 5

Nope, I have just told you the definition of i

Answer 6

Ohh so then what do u do

Answer 7

Tell me, what's \(i ^2\) ?

Answer 8

-1

Answer 9

Good, have you worked with radicals ?
particularly problems involving rationalization of denominator ???

Answer 10

Yes I believe I have

Answer 11

Great, we'll do the same thing here. Why don't you try??
Notice that we have a radical in numerator and denominator, only change is it's root of -1

Answer 12

@jay847 Have you tried ?

Answer 13

Yes but I can't get it

Answer 14

Ok, I'll help you

Answer 15

Ok:)

Answer 16

A complex no. is of the form
\[a+ib\]
a= real part
b= imaginary part
Conjugate of a complex no. is
\[a-ib\]
so \(a+ib\) and \(a-ib\) are complex conjugates of each other.
Do you get this ?

Answer 17

Sort of

Answer 18

We have
\[\frac{4+2i}{1-3i}\]
Multiply numerator and denominator by conjugate of denominator
which is ???

Answer 19

Do u mean 4x-3i

Answer 20

So u cross multiply

Answer 21

Complex conjugate of (1-3i) ???

Answer 22

-2??

Answer 23

If I have 1-3x, can you simplify that ?

Answer 24

No because there not like terms

Answer 25

Yeah, similarly here also because of i (\(\sqrt{-1}\) ) we can't simplify it.

Answer 26

So how do we solve it

Answer 27

First step is to find complex conjugate,
\[a+ib=> a-ib\]
\[a-ib=>a+ib\]
\[1-3i=> ????\]

Answer 28

4+2i

Answer 29

how do you say that ?

Answer 30

😣

Answer 31

Complex conjugate of a-ib is a+ib
\[a-ib=>a+ib\]
a=1
b=3
\[1-3i=>\]

Answer 32

1+3i

Answer 33

Good, do you get my point ?
it's same as conjugate of radicals
\[1+\sqrt 3\longrightarrow 1-\sqrt 3\]

Answer 34

Ok I get it

Answer 35

Now multiply numerator and denominator by conjugate of denominator

Answer 36

So I multiply both by 1+3i

Answer 37

yes :)

Answer 38

Do I have to foil

Answer 39

Yes :)

Answer 40

Ok thank you

Answer 41

Do you understand this ?

Answer 42

Yea thanks

Answer 43

:D