(2-i).jpeg "(2+3i)(2-i)")
Multiplying Complex Numbers: (2 + 3i)(2 - i)
This article will explore the multiplication of complex numbers using the example of (2 + 3i)(2 - i).
Understanding Complex Numbers
Complex numbers are numbers of 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
To multiply complex numbers, we use the distributive property, just like with real numbers.
Step 1: Distribute
(2 + 3i)(2 - i) = 2(2 - i) + 3i(2 - i)
Step 2: Simplify
= 4 - 2i + 6i - 3i²
Step 3: Substitute i² = -1
= 4 - 2i + 6i - 3(-1)
Step 4: Combine real and imaginary terms
= 4 + 3 + (-2 + 6)i
Step 5: Final answer
= 7 + 4i
Conclusion
Therefore, the product of (2 + 3i) and (2 - i) is 7 + 4i. This example demonstrates how to multiply complex numbers using the distributive property and the fundamental property of the imaginary unit (i² = -1).