 Hello and welcome to the session. In this session we will represent addition and subtraction of complex numbers genetically on complex plane. First of all let us discuss addition of complex numbers and complex plane. Now we know that any complex number is written as what is equal to x plus i eta y where x y belong to the set of real numbers. Also x is called the real part and y is called the imaginary part of this complex number. Also we can represent the complex number x plus i eta y as ordered pair x y. So on this eigen plane all we can say on this complex plane the point p with coordinates x y represents the complex number x plus i eta y where x represents the real part and y represents the imaginary part of the given complex number that is the complex number x plus i eta y. Now we will represent addition of two complex numbers on complex plane. Now suppose we have complex number z 1 is equal to 3 plus i eta and complex number z 2 is equal to 1 minus 5 i eta. Now we will represent some of these two complex numbers that is z 1 plus z 2 on complex plane. First of all let us represent complex number z 1 which is equal to 3 plus i eta on complex plane. Now for this complex number real part is equal to 3 and imaginary part is equal to 1. So we will move 3 units right and 1 unit up from original and we reach at this point let this point be p. So we have obtained point p with coordinates 3 1 which represents the complex number z 1 which is equal to 3 plus i eta. Now join op now we will draw complex number z 2 which is equal to 1 minus 5 i eta on complex plane. Now here we see that real part of this complex number is 1 and imaginary part is minus 5. So we will move 1 unit right and 5 units down and we reach at this point let this point be q. So we have this point q with coordinates 1 minus 5 which represents the complex number z 2 which is equal to 1 minus 5 i eta. Now join op now let us complete the parallelogram. Now op r q is the parallelogram. Now from original join the diagonal op r. Now this point r represents the addition of the 2 complex numbers that is z 1 plus z 2 and here you can see we moved 4 units to the right and 4 units downwards from original to reach the point r. Thus point r has coordinates 4 minus 4. So it is complex number 4 plus or minus 4 i eta that is 4 minus 4 i eta. So z 1 plus z 2 is equal to 4 minus 4 i eta. Now we can check our answer by actual addition. Now z 1 plus z 2 is equal to 3 plus i eta the whole plus of 1 minus 5 i eta the whole and this is equal to 3 plus i eta plus 1 minus 5 i eta. Now combining real and imaginary parts this is equal to 3 plus 1 that is 4 plus i eta minus 5 i eta that is minus 4 i eta. So we have obtained z 1 plus z 2 is equal to 4 minus 4 i eta. Now let us discuss subtraction of complex numbers on complex plane. Now if z 1 is equal to x plus i eta y then minus z 1 is equal to minus of x plus i eta y that is equal to minus x minus i eta y. Now here you can see in minus z 1 the sign of x and y are opposite to the sign of z 1 or to represent minus z 1 in complex plane it is drawn in opposite direction of z 1 that with same magnitude. Now let us take some complex numbers that is we have z 1 is equal to 3 plus i eta and z 2 is equal to 1 minus 5 i eta. Now we have to represent the difference that is z 1 minus z 2 on the complex plane. Now we have already drawn z 1 and z 2 on the complex plane. Now to find z 1 minus z 2 we first draw minus z 2 that is equal to minus of 1 minus 5 i eta the whole which is equal to minus 1 plus 5 i eta on the complex plane. Now real part of this complex number is minus 1 and imaginary part is 5. So we move 1 unit left and 5 units up from origin to reach this point let this be point q dash with coordinates minus 1 5 which represents the complex number minus z 2 which is equal to minus 1 plus 5 i eta. Now here you can see that minus z 2 is in opposite direction of z 2 and of same magnitude. Now let us complete the parallelogram. So we have completed the parallelogram o p r q dash and draw the diagonal r. Now this point r represents the subtraction of the two complex numbers that is z 1 minus z 2 and here you can see we have moved 2 units right and 6 units up from origin to reach point r thus point r has coordinates 2 6 so it is complex number 2 plus 6 i eta thus z 1 minus z 2 is equal to 2 plus 6 i eta. Now we can check our answer by action subtraction now z 1 minus z 2 is equal to 3 plus i eta the whole minus of 1 minus 5 i eta the whole which is equal to 3 plus i eta minus 1 plus 5 i eta. Now combining the real and imaginary parts we have 3 minus 1 that is equal to 2 plus i eta plus 5 i eta that is equal to plus 6 i eta. So z 1 minus z 2 is equal to 2 plus 6 i eta. So in general if z 1 and z 2 are two complex numbers and the points p and q represent the two numbers then by completing the parallelogram and drawing the diagonal point r will represent complex number z 1 plus z 2 and in difference z 1 minus z 2 minus z 2 is additive inverse of z 2 and points p and q dash represent complex numbers z 1 and minus z 2 respectively then completing parallelogram and drawing the diagonal point r will represent the complex number z 1 minus z 2. So in this session we have discussed how to represent adhesion and suppression of complex numbers geometrically on complex plane and this completes our session hope you all have enjoyed the session.