For {z: |z+3-3i| = 2} determine the minimum possible value of |z|

Question

zehanz · Answer

You can consider  {z: |z+3-3i| = 2}  as the complex numbers that have a distance of 2 units to the number -3+3i. 
So it represents a circle with radius 2 and center -3+3i. See attached image.
Now you have to look for the number (point on the circle) that is nearest to the origin.

anonymous · Answer

I seee thank you... how can I obtain the exact answer?

zehanz · Answer

Draw a line from the center to the origin.
The intersection with the circle is the number you are looking for.

anonymous · Answer

The problem is that the answer is $$3\sqrt{2}-2$$ and you can't really do that by hand :S

anonymous · Answer

Oh I know... I could convert the equation of the circle to a cartesian equation and plot y=-x as well and find the intersection. Thanks for your help :)

zehanz · Answer

YW!