(3i).jpeg "(6+2i)(3i)")
Multiplying Complex Numbers: (6 + 2i)(3i)
This article explores the multiplication of complex numbers, specifically the expression (6 + 2i)(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, just like we would with any binomial multiplication.
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Distribute: (6 + 2i)(3i) = 6(3i) + 2i(3i)
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Simplify: = 18i + 6i²
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Substitute i² = -1: = 18i + 6(-1)
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Combine Real and Imaginary Terms: = -6 + 18i
Result
Therefore, the product of (6 + 2i) and (3i) is -6 + 18i.
Key Points
- Complex number multiplication involves multiplying both the real and imaginary components of the numbers.
- The distributive property is essential in simplifying these multiplications.
- Remember that i² = -1.
This example demonstrates a straightforward approach to multiplying complex numbers. It's a fundamental operation in various mathematical applications, particularly in areas like electrical engineering and quantum mechanics.