If `|z-1|=1,` where z is a point on the argand plane, show that`(z-2)/(z)=i tan (argz),where i=sqrt(-1).`

If arg z = alpha and given that |z-1|=1, where z is a point on the argand plane , show that |(z-2)/z| = |tan alpha |,

If z is a complex number in the argand plane, then the equation |z-2|+|z+2|=8 represents

If |z^(2)-1|=|z|^(2)+1 , then z lies on :

Find the gratest and the least values of |z_(1)+z_(2)|, if z_(1)=24+7iand |z_(2)|=6," where "i=sqrt(-1)

Find the arguments of z_(1)=5+5i,z_(2)=-4+4i,z_(3)=-3-3i and z_(4)=2-2i, where i=sqrt(-1).

If z=x+i y is a variable complex number such that arg ((z-1)/(z+1))=(pi/4) , then

Let z be a non-real complex number lying on |z|=1, prove that z=(1+itan((arg(z))/2))/(1-itan((arg(z))/(2))) (where i=sqrt(-1).)

If z is such that |z-2 i|=2 sqrt(2) , then arg ((z-2)/(z+2))=

If P(x, y) denotes z=x+i y in Argand's plane and |(z-1)/(z+2 i)|=1 , then the locus of P is/an

Find the principal value of the arguments of z_(1)=2+2i,z_(2)=-3+3i,z_(3)=-4-4iand z_(4)=5-5i,where i=sqrt(-1).