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, prove that a + b = ( ) . Let z = – i , z = – + i. Find Re z z z  , Im z z . Find the modulus and argument of the complex number . Find the real numbers x and y if ( x – iy ) ( + i ) is the conjugate of – – i . . Find the modulus of + . . If ( x + iy ) = u + iv , then show that ( – u v . If α and β are different complex numbers with β = , then find β α αβ – – . Find the number of non-zero integral solutions of the equation – i . If ( a + ib ) ( c + id ) ( e + if ) ( g + ih ) = A + i B, then show that ( a + b ) ( c + d ) ( e + f ) ( g + h ) = A + B . If m – i , then find the least positive integral value of m . MATHEMATICS