(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Draw an argand diagram to represent the follwing property:

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

2. Relevant equations

z = x+iy;

real(z) = x

abs(z) = sqrt(x^2 + y^2)

img(z) = y

3. 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.

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# Homework Help: Representation of properties of Complex Numbers in Argand Diagrams

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