How to use distributive law to multiply complex numbers (2+3i)(1-5i)?
We'll recall the definition of the distributive law:
(a+b)(c+d)=(a+b)*c + (a+b)*d
We'll use the distributive law to perform the multiplication of given complex numbers:
(2+3i)(1-5i) = (2+3i)*1 + (2+3i)*(-5i)
We'll remove the brackets:
(2+3i)(1-5i) = 2 + 3i - 10i - 15 `i^2`
But `i^2` = -1
(2+3i)(1-5i) = 2 + 3i - 10i + 15
We'll combine real parts and imaginary parts and we'll get:
(2+3i)(1-5i) = 17 - 7i
The result of multiplication of the given complex numbers, using distributive law, is (2+3i)(1-5i) = 17 - 7i.