Multiplying Complex Numbers: (7 + 2i)(6 + 8i)
This article will guide you through the process of multiplying two complex numbers: (7 + 2i)(6 + 8i).
Understanding Complex Numbers
Complex numbers are numbers that consist of a real part and an imaginary part. They are typically written 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 (i.e., i² = 1).
Multiplication Process
To multiply complex numbers, we follow the distributive property, just like multiplying binomials.

Expand the product: (7 + 2i)(6 + 8i) = 7(6 + 8i) + 2i(6 + 8i)

Distribute: = 42 + 56i  12i + 16i²

Simplify using i² = 1: = 42 + 56i  12i  16

Combine real and imaginary terms: = (42  16) + (56  12)i

Final result: = 58 + 44i
Therefore, the product of (7 + 2i)(6 + 8i) is 58 + 44i.