Question

Given that Z1 = 1 + i and Z2 = 3 - 4i, find z1z2

Answer 1

7-i

Explanation:

It is asking for the product of the given complex numbers.

Z1Z2 means Z1 times Z2

(1+i)(3-4i)

You can do the whole foil thing here since we are multiplying a pair of binomials. But all you are doing when you do that is multiplying every term in the first ( ) to every term in the second ( ).

1(3)+1(-4i)+i(3)+i(-4i)

Simplify each term. That is, perform the multiplication in each term:

3-4i+3i-4i^2

Combine like terms and also replace i^2 with (-1):

3-1i-4(-1)

Multiplication identity property used:

3-i+4

Combine like terms:

7-i