(-2i)(5i).jpeg "(3i)(-2i)(5i)")
Simplifying Complex Number Multiplication: (3i)(-2i)(5i)
This article will guide you through the process of simplifying the multiplication of complex numbers: (3i)(-2i)(5i).
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.
Simplifying the Expression
Let's break down the multiplication step-by-step:
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Multiply the first two factors: (3i)(-2i) = -6i²
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Substitute i² with -1: -6i² = -6(-1) = 6
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Multiply the result by the third factor: 6(5i) = 30i
Therefore, the simplified form of (3i)(-2i)(5i) is 30i.
Key Points to Remember
- i² = -1 is a fundamental property of complex numbers.
- The product of two complex numbers is another complex number.
- Remember to treat 'i' as a variable when multiplying.
By understanding these concepts, you can easily simplify any multiplication involving complex numbers.