If the argument of ( z − a ) ( z ˉ − b ) is equal to that of 1 + i ( 3 + i ) ( 1 + 3 i ) , where a , b are real numbers. If locus of z is a circle with centre 2 3 + i then find ( a + b ) .

Question

If the argument of ( z − a ) ( z ˉ − b ) is equal to that of 1 + i ( 3 ​ + i ) ( 1 + 3 ​ i ) ​ , where a , b are real numbers. If locus of z is a circle with centre 2 3 + i ​ then find ( a + b ) .

TestHub · Accepted Answer

tan − 1 x 2 + y 2 − ( a + b ) x + ab ( a − b ) y ​ = 4 π ​ ⇒ ​ x 2 + y 2 − ( a + b ) x − ( a − b ) y + ab = 0 ​ ​ C e n t re = 2 3 + i ​ ⇒ a + b = 3

Mathematics - Complex Number Question with Solution | TestHub

Doubts & Discussion