How to use distributive law to multiply complex numbers (2+3i)(1-5i)?

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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.

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