(2i)(-7i).jpeg "(i)(2i)(-7i)")
Multiplying Complex Numbers: (i)(2i)(-7i)
This article will guide you through the process of multiplying the complex numbers (i)(2i)(-7i).
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 the Complex Numbers
Let's break down the multiplication:
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(i)(2i): Multiply the coefficients and the imaginary units. (i)(2i) = 2i² Since i² = -1, we have: 2i² = 2(-1) = -2
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(-2)(-7i): Now multiply the result from step 1 by -7i. (-2)(-7i) = 14i
The Answer
Therefore, the product of (i)(2i)(-7i) is 14i.
Key Points
- Remember that i² = -1.
- Multiply the coefficients and imaginary units separately.
- Simplify the result by replacing i² with -1.