Addition and Subtraction of Complex Numbers | Basic Operations On Complex Numbers Urdu

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In this video you will learn that " Addition and Subtraction of Complex Numbers | Basic Operations On Complex Numbers Urdu | Sir Naimat "

What is a complex number?
The number i
is defined to be such that i2=−1
. It is called an imaginary number because, unlike the natural numbers and the real numbers, it has no immediate physical interpretation. (Note that some books use j , instead of i ( So beware!)

A complex number is written in the form a+bi
where a,b∈R
. Here, a is the real part of the complex number and b is the imaginary part. (Note that i is not included when we refer to the imaginary part.) We also use the following notation to extract the real and imaginary parts:
Where z=a+bi, Re(z)=a and Im(z)=b
For convenience, if b=1 , we simply write a+i instead of a+1i
. If a=0 we simply write bi instead of 0+bi
. Of course, when a=0 and b=1
, we get just the imaginary number i
Examples
If z=3−4 , then Re(z)=3 and Im(z)=−4
If w=2i, then Re(w)=0 and Im(w)=2
.If u=−5, then Re(u)=−5 and Im(u)=0

The standard symbol for the set of all complex numbers is C, and we'll also refer to the complex plane as C.
We'll try to use x and y for real variables, and z and w for complex variables. For example, the equation z = x + yi is to be understood as saying that the complex number z is the sum of the real number x and the real number y times i. In general, the x part of a complex number z = x + yi is called the real part of z, while y is called the imaginary part of z. (Sometimes yi is called the imaginary part.)

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When we use the xy-plane for the complex plane C, we'll call the x-axis by the name real axis, and the y-axis we'll call the imaginary axis.

Real numbers are to be considered as special cases of complex numbers; they're just the numbers x + yi when y is 0, that is, they're the numbers on the real axis. For instance, the real number 2 is 2 + 0i. The numbers on the imaginary axis are sometimes called purely imaginary numbers.

Arithmetic operations on C
The operations of addition and subtraction are easily understood. To add or subtract two complex numbers, just add or subtract the corresponding real and imaginary parts. For instance, the sum of 5 + 3i and 4 + 2i is 9 + 5i. For another, the sum of 3 + i and –1 + 2i is 2 + 3i.
.

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