(5-4i).jpeg "(3i)(5-4i)")
Multiplying Complex Numbers: (3i)(5-4i)
This article will guide you through the process of multiplying the complex numbers (3i) and (5-4i).
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).
Multiplying Complex Numbers
To multiply complex numbers, we use the distributive property, just like with real numbers. This means we multiply each term in the first complex number by each term in the second complex number.
Step-by-Step Solution
Let's break down the multiplication of (3i)(5-4i):
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Distribute: (3i)(5-4i) = (3i * 5) + (3i * -4i)
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Simplify: = 15i - 12i²
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Substitute i² with -1: = 15i - 12(-1)
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Combine terms: = 12 + 15i
Result
Therefore, the product of (3i)(5-4i) is 12 + 15i. This is also a complex number expressed in the form a + bi, where a = 12 and b = 15.
Conclusion
Multiplying complex numbers can be achieved by applying the distributive property and then simplifying the result by substituting i² with -1. Remember that the product of two complex numbers is also a complex number.