(4-5i)(4+i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (4-5i)(4+i)

This article will guide you through multiplying two complex numbers: (4-5i)(4+i).

Understanding Complex Numbers

Complex numbers are numbers that consist of a real part and an imaginary part. They are written in the form a + bi, where 'a' and 'b' are real numbers, and 'i' represents the imaginary unit, where i² = -1.

Multiplying Complex Numbers

When multiplying complex numbers, we treat them like binomials and use the distributive property (or FOIL method).

Here's how to multiply (4-5i)(4+i):

1. FOIL Method:

   • First: (4)(4) = 16
   • Outer: (4)(i) = 4i
   • Inner: (-5i)(4) = -20i
   • Last: (-5i)(i) = -5i²

2. Combine Like Terms:

   • 16 + 4i - 20i - 5i²

3. Simplify:

   • Remember that i² = -1, so we substitute: 16 + 4i - 20i - 5(-1)
   • Combine the real and imaginary terms: 16 + 5 + 4i - 20i = 21 - 16i

Therefore, the product of (4-5i)(4+i) is 21 - 16i.