Complex Numbers

Question

I don't understand what I am suppose to do.

 

Determine the prodcut of the given complex number.

a) 4-i, 4+i

 

The complex numbers get a lot harder, but this is the basis/

Answer 1

Apply the distributive property just like you would when multiplying real numbers.

 

(4 - i)(4 + i) = 4² + 4i - i4 - i² = 16 - i² = 16 - (-1) = 16 + 1 = 17

 

You could have also used the fact that the problem gives you the factored form of a difference of squares:

 

(4 - i)(4 + i) = 4² - i² = 16 - (-1) = 17