Question

using the properties of complex numbers, what is the result of the calculation (2 + 3i) (4 - i) + (1 + 5i)

Answer 1

Compute the product then add:

(2+3i)(4−i) = 2·4 + 2·(−i) + 3i·4 + 3i·(−i)
= 8 − 2i + 12i − 3i^2
= 8 + 10i − 3(−1) (since i^2 = −1)
= 8 + 10i + 3
= 11 + 10i.

Now add (1 + 5i): (11 + 10i) + (1 + 5i) = 12 + 15i.