Simplifying Complex Numbers: (5  9i)  (1 + 4i)
This article will guide you through simplifying the expression (5  9i)  (1 + 4i). This involves understanding the basics of complex numbers and how to perform operations with them.
What are Complex Numbers?
Complex numbers are numbers that extend the real number system by including the imaginary unit i, where i² = 1. They are typically expressed in the form a + bi, where a and b are real numbers.
Simplifying the Expression

Distribute the negative sign: (5  9i)  (1 + 4i) = 5  9i  1  4i

Combine the real and imaginary terms: (5  1) + (9  4)i = 4  13i
Therefore, the simplified form of (5  9i)  (1 + 4i) is 4  13i.
Conclusion
This example showcases a straightforward simplification of a complex number expression. Remember, when dealing with complex numbers, always treat i as a variable, and follow the rules of algebra to combine like terms.