Given that `|z-1|=1,` where z is a point
on the argand planne , show that `(z-2)/(z)=itan (arg z),`
where `i=sqrt(-1).`

The equation z^(2)-i|z-1|^(2)=0, where i=sqrt(-1), has.

Solve the equation |z|+z=2+i, where z = x + iy.

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

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).)

Find the center and radius of the circle 2zbarz+(3-i)z+(3+i)z-7=0," where " i=sqrt(-1).

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

If |z-iRe(z)|=|z-Im(z)|, then prove that z lies on the bisectors of the quadrants, " where "i=sqrt(-1).

Consider the curves on the Argand plane as " "{:(C_(1):arg(z)=pi/4","),(C_(2):arg(z)=(3pi)/(4)):} and C_(3):arg(z-5-5i)=pi," where " i=sqrt(-1). bb"Statement-1" Area of the region bounded by the curves C_(1),C_(2) " and " C_(3) " is " 25/2 bb"Statement-2" The boundaries of C_(1),C_(2) " and " C_(3) constitute a right isosceles triangle.

If iz^3+z^2-z+i = 0 , then show that |z|=1.

If z_(1),z_(2)andz_(3) are the vertices of an equilasteral triangle with z_(0) as its circumcentre , then changing origin to z^(0) ,show that z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=0, where z_(1),z_(2),z_(3), are new complex numbers of the vertices.