Fill in the blanks of the following
(i) For any two complex numbers z1, z2 and any real numbers a, b,
|az1−bz2|2 +| bz1+ az2|2 = ............
(ii) The value of −√25 * √−9 is...........
(iii) The number (1-i)3/(1-i3) is equal to ...............
(iv) The sum of the series i + i2 + i3 + ... upto 1000 terms is ..........
(v) Multiplicative inverse of 1 + i is ................
(vi) If z1 and z2 are complex numbers such that z1 + z2 is a real number, then z2 = ....
(vii) arg (z) + arg (Bar)z (Bar z ≠ 0) is ...............
(viii) If |z + 4| ≤ 3 , then the greatest and least values of |z +1| are ..... and .....
(ix) If|(z-2)/(z+2)| =π/6 , then the locus of z is ............
(x) If |z| = 4 and arg (z) =5π/6, then z = ............
