(-7i)(2i).jpeg "(-3i)(-7i)(2i)")
Simplifying Complex Number Multiplication: (-3i)(-7i)(2i)
This article will guide you through the process of simplifying the multiplication of complex numbers: (-3i)(-7i)(2i).
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.
Multiplying Complex Numbers
To multiply complex numbers, we treat them as binomials and use the distributive property (or FOIL method). However, remember that i² = -1.
Solving the Problem
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Start by multiplying the first two complex numbers: (-3i)(-7i) = 21i²
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Substitute i² with -1: 21i² = 21(-1) = -21
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Now, multiply the result by the remaining complex number: -21 (2i) = -42i
Final Answer
Therefore, the simplified form of (-3i)(-7i)(2i) is -42i.
Key Takeaways
- Remember that i² = -1.
- Use the distributive property (or FOIL method) to multiply complex numbers.
- Simplify the expression by substituting i² with -1.