(-2i)(4i).jpeg "(3i)(-2i)(4i)")
Multiplying Complex Numbers: (3i)(-2i)(4i)
This article will guide you through the process of multiplying the complex numbers (3i)(-2i)(4i).
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 Complex Numbers
When multiplying complex numbers, we follow the same rules as with regular multiplication, but we need to keep in mind the special property of 'i':
- i² = -1
Solving (3i)(-2i)(4i)
- Multiply the first two factors: (3i)(-2i) = -6i²
- Substitute i² with -1: -6(-1) = 6
- Multiply the result with the remaining factor: 6(4i) = 24i
Therefore, the product of (3i)(-2i)(4i) is 24i.
Key Points
- Remember the special property of 'i': i² = -1
- Treat complex number multiplication like regular multiplication, but be mindful of the 'i' term.
- The result of multiplying the given complex numbers is a purely imaginary number, 24i.