(3i).jpeg "(2i)(3i)")
Understanding Complex Number Multiplication: (2i)(3i)
In the realm of mathematics, complex numbers play a crucial role, particularly in fields like electrical engineering, quantum mechanics, and signal processing. Complex numbers are represented in the form of a + bi, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit, defined as the square root of -1.
Multiplying Complex Numbers
Multiplying complex numbers follows the distributive property, similar to multiplying binomials. When multiplying two complex numbers, we essentially expand the expression and simplify it using the fact that i² = -1.
Solving (2i)(3i)
Let's delve into the multiplication of (2i)(3i):
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Direct Multiplication: (2i)(3i) = 6i²
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Substituting i²: Since i² = -1, we substitute it: 6i² = 6(-1)
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Simplifying: 6(-1) = -6
Therefore, the product of (2i)(3i) is -6.
Key Takeaway
The multiplication of complex numbers involves treating the imaginary unit 'i' as a variable, applying the distributive property, and simplifying the result using the property i² = -1. This process allows us to obtain a real number as the result, even though we began with imaginary terms.