Before starting the division of a complex number, we have to go to another important concept called
the conjugate of a complex number.
So if complex number is explosive, e.g., the conjugate is X minus.
Now you can see the difference between a complex number and its conjugate is the change of sine only
of its imaginary part.
The sign of the real part remained the same in both the complex number and its conjugate only.
There is a sign of the imaginary part of the complex number.
So if the number is seven plus five, it is conjugate is seven minutes and the number is seven minus
five.
Then conjugate will be seven plus.
So both these numbers are conjugate of each other because in both this number that is assigned only
at the imaginary part.
Let's start the division.
Now we have to divide these two complex number Zetterlund and two, so these are the complex number
two plus three and seven plus five.
So how do we start the division?
So basically the first important step of the division is that you have to multiply and divide this number
with the complex conjugate of the denominator.
So the denominator of this division is seven plus five.
So you have to multiply this number and also divide this number with the complex conjugate of seven
plus five.
So this is a first step.
You have to multiply both the numerator and the denominator.
In the previous rebill, you have learned how to multiply the complex number.
So basically at the numerator you have to multipack with seven minus five.
And similarly, you have to multiply three digit seven minus five in the denominator.
You have an advantage.
This is seven plus five and this is seven minus five.
So you can use the famous algebraic expression A minus B impressed me is equals to square minus B square.
So this is A plus B, this is minus B, so in the denominator you will get A squared, minus B squared
and in the denominator you will multiply this group with seven minus five and these three with seven
minus five.
So when you solve this you will get 14, minus 20, plus 20 one day, minus 15 square.
So this square and this square, this becomes minus one.
So minus 15, minus one and minus twenty five in two.
Minus one.
So you will get 14, plus 11, plus 15.
And in the denominator you will get 14 less.
Twenty five to forty nine plus twenty five becomes seventy four.
And similarly 14, 15 becomes twenty nine.
Now in the last step you have to break this year.
So twenty nine over seventy four plus eleven did over seventy four.
So if you divide twenty nine with seventy four point three nine two and if you divide eleven by seventy
four you will get point one for it.
So this is the method of performing division with the complex number.
So most important concept is the first step where you multiply and divide the number with the complex
conjugate of the denominator and then the rest is very simple.
You just have to multiply the numerators with each other and denominators with each other and then you
have to simplify.