 Hi and welcome to the session. I am Asha and I am going to help you with the following question that says that z1 is equal to 2 minus iota and z2 is equal to minus 2 minus iota. Find real part of z1 into z2 upon z1 conjugate. For any complex number A plus iota B conjugate of z is denoted by z bar is equal to A minus iota B. With the help of this idea we are going to find the real part of z1 into z2 upon z1 conjugate therefore this is our key idea. Let us now begin with the solution. First let us find z1 into z2 upon z1 conjugate. Now z1 is 2 minus iota and z2 is minus 2 plus iota and z1 conjugate according to our key idea will be 2 plus iota since z1 is equal to 2 minus iota then z1 conjugate will be 2 plus iota. Now let us simplify it further on multiplying 2 with minus 2 we have minus 4, multiplying 2 with iota we have 2 iota and again plus 2 iota and minus iota square and in the denominator we have 2 plus iota which can further be written as minus 4 plus 4 iota plus 1 upon 2 plus iota which is further equal to minus 3 plus 4 iota upon 2 plus iota. Now let us try to remove i from the denominator so multiplying the numerator and denominator by the conjugate of 2 plus iota which is 2 minus iota we further have 2 square minus iota square and the numerator we have minus 3 plus 4 iota into 2 minus iota which is further equal to or multiplying minus 3 with 2 we have minus 6 plus 3 iota plus 8 iota minus 4 iota square upon 4 plus 1 since iota square is minus 1 this is further equal to minus 6 plus 11 iota and this is plus 4 again since iota square is minus 1 and in the denominator we have 5 which can further be written as minus 2 plus 11 iota upon 5 and how it is separate the real part and imaginary part so we have minus 2 upon 5 plus 11 upon 5 iota and now we are required to find the real part of z1 into z2 upon z1 conjugate which we have just now find so to find the real part of z1 into z2 upon z1 conjugate let us see what we have got the real part according to our clear idea will be minus 2 upon 5 and thus our answer is minus 2 upon 5 so this completes the solution hope you enjoyed it take care and have a good day