Suppose m = 2 + 6i, and , |m+n| = 3√10 where n is a complex number.

a. What is the minimum value of the modulus of n?

b. Provide one example of the complex number, n.

One example: n = -2 + (-6 + 3√10)i

|n| = √[(-2)^{2} + (-6 + 3√10)^{2}] = √[130 - 36√10] ≈ 4.02

Not sure I can prove this is a minimum though!