(3i)(i).jpeg "(-3i)(3i)(i)")
Simplifying Complex Number Multiplication: (-3i)(3i)(i)
This article will guide you through the process of simplifying the complex number multiplication: (-3i)(3i)(i).
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 Multiplication
-
Start by multiplying the first two factors: (-3i)(3i) = -9i²
-
Recall that i² = -1: -9i² = -9(-1) = 9
-
Now, multiply the result by the remaining factor (i): 9(i) = 9i
Final Answer
Therefore, the simplified form of (-3i)(3i)(i) is 9i.
Key Points
- Remember that i² = -1.
- When multiplying complex numbers, treat i like any other variable, but remember to simplify i² to -1.
- The final result of complex number multiplication is also a complex number.