Draw an argand diagram to represent the follwing property:
real(z) < abs(z) < real(z)+img(z)
z = x+iy;
real(z) = x
abs(z) = sqrt(x^2 + y^2)
img(z) = y
The Attempt at a Solution
substituting original expression with x, y, and sqrt(x^2 + y^2) two inequalities are obtained:
1. x^2 < x^2 + y^2; which simplifies to y > 0
2. x^2 + y^2 < x^2 + y^2 + 2*x*y which simplifies to x*y > 0
now the solution for the first inequality is clear: all the region in an argand diagram above the x-axis(real axis).
the second inequality remains unclear.