let’s take any natural number say 2 yes we can take two so can i right 2 as 2 + 0i so i can write natural number as a complex number let us take example of a whole number 0 0 , can be written as( zero + zero i) let us take example often integer say – 3, -3 can be written as (-3+0i) and if i take any real number any real number as in i can take any fraction or decimal value if i take 0.5, 0.5 can be written as 0.5 + 0i so what I want to conclude there is all these four values that is natural number whole number integers real numbers are nothing but complex numbers this is what the most important part of complex numbers is we have Z =a + ib there a is nothing but it is real part of z and it is denoted by RE of Z this part is very important from your entrance point of view they can ask you to find RE(Z)so what is RE(Z) nothing but a real part of Z and Ib is nothing but imaginary part of Z and it is denoted by Im (Z) now let us start some algebraic operations on complex numbers the first which we will be studying is addition of a complex numbers now consider the example you if Z1 & Z2 are two complex numbers ok Z1 has the value as a+ IB and Z2 has the value c +ID then that the edition will be given as that Z1 + Z2 is equal to a + C now that is I, I added the real part so i obtained it by adding the real part plus the imaginary parts will be added here this B plus D and I is common so you will gate I this is obtained by adding imaginary parts so the addition of the complex number turn out to be as( a + C + B + D)*. I now in the similar manner we will start with subtraction of a complex numbers same example let’s Z 1and Z2 be two complex numbers whose values are as follows then we will have Z1-Z2 as a – c that is we are subtracting the real part plus keep in mind about this positive sign the sign should not be – here it should Be plus the other term which we will obtain is b minus the other term will be D into I so this is obtained by subtracting the imaginary parts so keep in mind Z1- 82 is given by a – c plus B minus D into I.

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