(-8%2B3i).jpeg "(7-6i)(-8+3i)")
Multiplying Complex Numbers: (7-6i)(-8+3i)
This article will guide you through the process of multiplying the complex numbers (7-6i) and (-8+3i).
Understanding Complex Numbers
Complex numbers are numbers that can be expressed in the form a + bi, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit, defined as the square root of -1 (i² = -1).
Multiplying Complex Numbers
Multiplying complex numbers is similar to multiplying binomials. We use the distributive property (also known as FOIL - First, Outer, Inner, Last).
Let's multiply (7-6i) and (-8+3i):
(7-6i)(-8+3i) = 7(-8) + 7(3i) - 6i(-8) - 6i(3i)
Expanding the terms:
= -56 + 21i + 48i - 18i²
Remember that i² = -1. Substitute this into the equation:
= -56 + 21i + 48i - 18(-1)
Combining like terms:
= -56 + 18 + 21i + 48i
= -38 + 69i
Final Result
Therefore, the product of (7-6i) and (-8+3i) is -38 + 69i.