 Hello and welcome to the session. In this session we will discuss a question which says that illustrate the sum and difference of the given complex numbers geometrically. And the complex numbers are given to us as z1 is equal to minus 7 plus 4 iota, z2 is equal to minus 2 minus 7 iota. Also, find the sum and difference algebraically. Now let us start with the solution of the given question. Now in the question we are given the complex numbers z1 and z2. So given z1 is equal to minus 7 plus 4 iota and z2 is equal to minus 2 minus 7 iota. First of all let us find sum of these two complex numbers geometrically. Now let us draw complex number z1 which is equal to minus 7 plus 4 iota on complex plane. Now real part of this complex number is minus 7 and the imaginary part is fill, so we move 7 minutes to the left and 4 minutes up from the origin and we reach at this point, let this point be p. So this is the point p with coordinates minus 7 4 and this represents the complex number z1 which is equal to minus 7 plus 4 iota. Now we are given o p. Now let us draw the complex number z2 on the complex plane. Now real part of this complex number is minus 2 and imaginary part of this complex number is minus 7. So we move 2 minutes to the left of the region and we reach at this point and from this point we move 7 minutes downwards and we reach at this point, let this point be q. So this is the point q with coordinates minus 2 minus 7 which represents the complex number z2 that is equal to minus 2 minus 7 iota. Then we join o q. Now let us complete the parallelogram. Now o p r q is a parallelogram. Now from origin o draw the diagonal o r. This point r represents the addition of the two complex numbers that is z1 plus z2 we can see we moved 9 minutes left and 3 minutes down from origin o to reach the point r. Thus point r has coordinates minus 9 minus 3 this complex number whose real part is minus 9 and imaginary part is minus 3. So it will be minus 9 minus 3 iota. Thus z1 plus z2 is equal to minus 9 minus 3 iota. Now let us add the complex numbers and generally now z1 plus z2 is equal to minus 7 plus 4 iota plus of minus 2 minus 7 iota the whole. Now combining real and imaginary parts we have minus 7 minus 2 the whole plus of 4 minus 7 the whole into iota which is equal to minus 9 minus 3 iota. So we have obtained z1 plus z2 is equal to minus 9 minus 3 iota. Now let us find difference of the given complex numbers. Now we know that when we have to draw negative of a given complex number z that is minus z in the complex plane then we represent h by drawing it in opposite direction of z but at same distance from point o. Now here complex numbers z1 and z2 are given to us and we have to represent z1 minus z2 on the complex plane. Now we have already drawn complex numbers z1 and z2 on the complex plane. Now to find z1 minus z2 we first draw minus z2 that is equal to minus of minus 2 minus 7 iota the whole which is equal to 2 into 7 iota. Here the real part of this complex number is 2 and imaginary part is 7. So we move 2 units right and 7 units up from the point o and we reach at this point. Let this point be q dash and here we have the point q dash which coordinates 2, 7 which represents the complex number minus z2 which is equal to 2 plus 7 iota. Now here you can see that the complex number minus z2 is in opposite direction of the complex number z2 and at same distance from the point o that is origin. Now let us complete the parallelogram. o p r q dash is a parallelogram. Now draw the diagonal o r. This point r represents the reflection of the 2 complex numbers that is z1 minus z2. Now see we have moved 5 units left and 11 units up from the point o to reach the point r. Thus point r has coordinates minus 5, 11 so it is complex number minus 5 plus 11 iota. Thus z1 minus z2 is equal to minus 5 plus 11 iota. Now let us find the difference as regularly. z1 minus z2 is equal to minus 7 plus 4 iota the whole minus of minus 2 minus 7 iota the whole. Now combining real and imaginary parts this is equal to minus 7 plus 3 the whole plus of 4 plus 7 the whole into iota which is equal to minus 5 plus 11 iota. So difference of the 2 complex numbers that is z1 minus z2 is equal to minus 5 plus 11 iota. So this is the solution of the given question. That's all for this session. Hope you all have enjoyed the session.