Question

Can someone please explain how to find out the greatest value of |z|?

Answer 1

Okay, so I have a circle with centre (0,2) with radius 2. And a line starting at -2 making an angle of 45 degrees with the real axis.

Answer 2

But how do I calculate the greatest value of |z|?

Answer 3

Use the law of cosines to find the largest side of the isosceles triangle of vertex (0,2) and one of its side the line from the origin to the point (0,2)
Let a be the largest side then
\[
a^2 = 2^2 + 2^2 - 2(2)2 \cos(135)
\]

Answer 4

You can finish the rest

Answer 5

The exact value of max of |z| is
\[
\sqrt{8+4 \sqrt{2}}
\]

Answer 6

Which is about
3.69552

Answer 7

cos 135? How so? :O

Answer 8

180-45=135

Answer 9

Oh okay. Got it. Thank you so much. (: