Question

3. 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.
Answer:

Answer 1

Explanation:

Suppose m = 2 + 6i, and |m+n|=3√10,

The modulus sign means m+n can either be positive or negative as shown.

If it is positive:.2+6i+n = 3√10

n = 3√10-(2+6i)

n = 3√10-2-18√10i

n = (-2+3√10)+√10i

b) Example of the complex number is given as (-2+3√10)+√10i. This is a complex number because it contains the real part and the imaginary part.