 Hello and welcome to the session. In this session we will discuss a question which says that if the complex formula z1 is equal to 4 plus 2 iota and the complex formula z2 is equal to 2 plus 6 iota, plot the number z1 plus z2 also show that modulus of z1 plus modulus of z2 is greater than modulus of z1 plus z2. Now before starting the solution of this question you should know a result and that is the modulus of any complex number z such that z is equal to a plus b iota where b belongs to the set of real numbers is given by modulus of z is equal to modulus of a plus b iota which is equal to square root of a square plus b square. Therefore the modulus of this number distance from the origin to this point. Now this result will work out as a key idea for solving out this question and now we will start with the solution. Now z1 and z2 are given to us so given now z1 plus z2 will be equal to 4 plus 2 iota the whole plus 2 is equal to 4 plus 2 the whole 2 times 6 iota the whole and this is equal to 6 z1 is equal to 4 plus 2 iota by the point whose coordinates are z2 which is equal to iota by the point b which coordinates are 2 6 and we will represent z1 plus z2 which is equal to 6 plus 8 iota by the point whose coordinates are c b and c on the graph. Now we have plotted the points a b and c on the graph that is a is representing the number z1 this point b is representing the number z2 and this point c is representing the number z1 plus z2. Now using this result which is given in the key idea this is z1 then modulus of z1 will be equal to square root which is 4 square plus b square which is 2 square which is equal to square root of 16 plus 4 which is equal to root 20 which is further with z1 the distance of the point z1 from the region so this is equal to now this is z2 so modulus of z2 will be equal to square root of a square which is b square which is 6 square this will be equal to square root of 4 plus 36 which is equal to now here the distance of the point z2 from the region so this distance is equal to z2 is equal to modulus of z1 plus z2 is equal to square root which is 6 square plus b square which is 8 square and this is equal to square root of 34 which is equal to which is equal to 10 now here also this is the distance from the region now here the distance of this point that is z1 z2 the region is equal to now this is modulus of z1 this is modulus of z2 therefore z1 plus z2 is greater than 10 therefore o b is greater than o c hence modulus of z1 plus z2 is greater than modulus of z1 plus z2 of the given question and that is all for this session hope you all have enjoyed this session