(7i).jpeg "(2i)(7i)")
Multiplying Imaginary Numbers: (2i)(7i)
This article will walk through the process of multiplying two imaginary numbers: (2i)(7i).
Understanding Imaginary Numbers
Imaginary numbers, denoted by the symbol i, are a fundamental concept in mathematics. They are defined as the square root of -1, meaning i² = -1. This concept is crucial for solving equations that have negative values under the square root.
Multiplying Imaginary Numbers
To multiply imaginary numbers, we follow the same rules as multiplying any other algebraic expressions:
- Multiply the coefficients: 2 * 7 = 14
- Multiply the imaginary units: i * i = i²
Since we know i² = -1, we can substitute:
(2i)(7i) = 14 * (-1) = -14
Therefore, the product of (2i) and (7i) is -14.
Key Takeaway
Multiplying imaginary numbers involves the same principles as multiplying any other algebraic expressions. The key difference is the substitution of i² = -1, which can significantly change the outcome of the multiplication.