साबित करें कि निम्नलिखित असमानताएं:(i) |(z)/(|z|) -1| ले |आर्ग z| (ii) |z-1|le|z| |आर्ग z | + |z|-1...

Prove that following inequalities: (i) |(z)/(|z|) -1| le |arg z| (ii) |z-1|le|z| |arg z | + |z|-1|

If |z - 1| = |z + 1| = |z - 2i|, then value of |z| is

if |z-1|=|z-i| then locus of z is

Find z , if |(z+1)/(z+i)|=1

For any complex number z, prove that: (i) -|z| le R_(e)(z)le|z| (ii) -|z|leI_(m)(z)le|z| .

if z_(1)=3+4i and z_(2)=12-5i , verify: (i) |-z_(1)|=|z_(1)| (ii) |z_(1)+z_(2)|lt|z_(1)|+|z_(2)| (iii) |z_(1)z_(2)|=|z_(1)||z_(2)| .

If z_(1)=5-7i and z_(2)=7-9i , verify: (i) |-z_(1)|=|z_(1)| (ii) |z_(1)z_(2)|=|z_(1)||z_(2)|

If |z+1| + |z-3| le 10 , then the range of values of |z - 7| is