(3i).jpeg "(11i)(3i)")
Simplifying Complex Numbers: (11i)(3i)
This article will guide you through the simplification of the product of two complex numbers: (11i)(3i).
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 (i.e., i² = -1).
Multiplying Complex Numbers
To multiply complex numbers, we treat them like binomials and apply the distributive property.
Let's simplify the given expression:
(11i)(3i) = (11 * 3) * (i * i)
= 33 * i²
= 33 * (-1)
= -33
Conclusion
Therefore, the product of (11i) and (3i) is -33. It is important to note that the result is a real number, even though the original numbers were imaginary. This is because multiplying two imaginary numbers results in a real number.