Multiplying Complex Numbers: (−2+4i)⋅(5+i)
This article will guide you through the process of multiplying two complex numbers: (2 + 4i) and (5 + i).
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).
Multiplication Process
To multiply complex numbers, we follow the same distributive property used for multiplying binomials:

FOIL Method: This stands for "First, Outer, Inner, Last". We multiply each term in the first complex number by each term in the second complex number:
 First: (2) * 5 = 10
 Outer: (2) * i = 2i
 Inner: 4i * 5 = 20i
 Last: 4i * i = 4i²

Simplify: Remember that i² = 1. Substitute this value and combine the real and imaginary terms:
 10  2i + 20i + 4(1)
 10  4 + 18i

Final Result: Combine the real terms and the imaginary terms:
 (2+4i)⋅(5+i) = 14 + 18i
Conclusion
Therefore, the product of (2 + 4i) and (5 + i) is 14 + 18i. By understanding the properties of complex numbers and applying the distributive property, we can effectively multiply complex numbers.