` If "|z-i|=1 &"Arg(z)=(pi)/(2)" then the "z" is (1) "-2i" (2) "0" (4) "2i"`

If |z-i|=1 and amp(z)=(pi)/(2)(z!=0), then z is

Fill in the blanks of the following . (i) For any two complex numbers z_(1), z_(2) and any real numbers a, b, |az_(1) - bz_(2)|^(2) + |bz_(1) + az_(2)|^(2) =* * * (ii) The value of sqrt(-25) xxsqrt(-9) is … (iii) The number (1 - i)^(3)/(1 -i^(3)) is equal to ... (iv) The sum of the series i + i^(2) + i^(3)+ * * * upto 1000 terms us ... (v) Multiplicative inverse of 1 + i is ... (vi) If z_(1) "and" z_(2) are complex numbers such that z_(1) + z_(2) is a real number, then z_(1) = * * * (vii) arg(z) + arg barz "where", (barz ne 0) is ... (viii) If |z + 4| le 3, "then the greatest and least values of" |z + 1| are ... and ... (ix) If |(z - 2)/(z + 2)| =(pi)/(6) , then the locus of z is ... (x) If |z| = 4 "and arg" (z) = (5pi)/(6), then z = * * *

Locus of z if arg[z-(1+i)]={(3 pi)/(4) when |z| |z-4| is

For |z-1=1,i tan((arg(z-1))/(2))+(2)/(z) is

If (pi)/(3) and (pi)/(4) are arguments of z_(1) and bar(z)_(2), then the value of arg (z_(1)z_(2)) is

If |z_(1)|=|z_(2)| and arg (z_(1)//z_(2))=pi, then find the of z_(1)z_(2).

If z_(1) and z_(2) are two non-zero complex number such that |z_(1)z_(2)|=2 and arg(z_(1))-arg(z_(2))=(pi)/(2) ,then the value of 3iz_(1)z_(2)

If z lies on the curve arg (z+i)=(pi)/(4) , then the minimum value of |z+4-3i|+|z-4+3i| is [Note :i^(2)=-1 ]

If z and w are two complex number such that |zw|=1 and arg(z)arg(w)=(pi)/(2), then show that bar(z)w=-i