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## Homework Statement

Draw an argand diagram to represent the follwing property:

real(z) < abs(z) < real(z)+img(z)

## Homework Equations

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.