Multiplying Complex Numbers: (9 + 4i)(2  3i)
This article will guide you through the process of multiplying two complex numbers: (9 + 4i) and (2  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).
Multiplication Process
To multiply complex numbers, we use the distributive property, similar to multiplying binomials:

Expand the product:
(9 + 4i)(2  3i) = 9(2  3i) + 4i(2  3i)

Distribute:
= 18  27i + 8i  12i²

Substitute i² with 1:
= 18  27i + 8i + 12

Combine real and imaginary terms:
= (18 + 12) + (27 + 8)i

Simplify:
= 30  19i
Conclusion
Therefore, the product of (9 + 4i) and (2  3i) is 30  19i. This demonstrates how to multiply complex numbers using the distributive property and the definition of the imaginary unit.