Expert: Ahmed Salami - 10/18/2010

Question
Write down the inequality abs(z+3-i)larger or equals to abs(z+i-3i) in cartesian form. I don't understand what form is it in now. Thanks heaps. =)

Answer
Hi Caleb,
The complex number z is written in cartesian form as
z = x + iy
The modulus (or magnitude) of z is written as
abs(z) = √(x² + y²)
So,
z+3-i = (x + iy) + 3 - i
= (x+3) + i(y-1)
abs(z+3-i) = √[(x+3)² + (y-1)²]

z+1-3i = (x + iy) + 1 - 3i
= (x+1) + i(y-3)
abs(z+1-3i) = √[(x+1)² + (y-3)²]

Regards