If z = x + iy, x,y real, then |x| + |y| `<=` k |z|, where k is equal to :

If z= x + iy, x, y real, prove that : |x|+|y| le sqrt2 |z| .

If z = x + iy and |z+6| = |2z+3| , prove that x^2+y^2 =9.

If z=x+iy , where x and y are real numbers and |x|+|y| lt= k|z| then k=.....

If x , y are real and x + iy=0 then

If z=x+iy , show that sqrt(2)|z| ge |x|+ |y| .

If z=x+iy prove that |\x|+|\y|lesqrt(2)|\z|

If z = x + iy and |2z+1|=|z-2i| ,then show that 3(x^(2)+y^(2))+4(x+y)=3

If z = x+iy, prove that arg(z -1) = tan^(-1)(y/(x-1)) and arg(z+1) = tan^(-1)(y/(x+1))

Let z=x+iy, where x and y are real. Thepoints (x,y) in the X-Y plane for which (z+i)/(z-i) is purely imaginary lie on