Math Chapter Wise question with answer

Q01 If (1 + i tanα)1+itanβ has real values only, then one of them is given by: English · UP PCS (Pre) 1996 Q02 The complex valued function f(z) = u(x,y) + iv(x,y), for z = x + iy, is analytic if and only if: English · OPSC PGT 2017 Q03 If ((()) (())) ((()) u x,y iv x,y, forz 0 f z 0, forz 0 + ≠ = where ((()) 3 3 2 2 x y u x,y, x y − = + (()) 3 3 2 2... English · LT 2018 Q04 If r r r Z cos isin, 2 2 then Z1.Z2.Z3....∞ ∞ ∞ is equal to: English · UP PCS (Pre) 2003 Q05 The Real part of sin (x+iy) is: English · TGT 2010 Q06 The function f (z) = |z|2 is English · Bihar (TRE 1.0) -2023