(2i).jpeg "(6i)(2i)")
Simplifying Complex Numbers: (6i)(2i)
This article will guide you through simplifying the product of two complex numbers, specifically (6i)(2i).
Understanding Complex Numbers
Complex numbers are numbers that extend the real number system by including the imaginary unit i, where i² = -1. They are typically written in the form a + bi, where a and b are real numbers.
Multiplying Complex Numbers
To multiply complex numbers, we treat them like binomials and use the distributive property:
(a + bi)(c + di) = ac + adi + bci + bdi²
Since i² = -1, we can substitute this value:
(a + bi)(c + di) = ac + adi + bci - bd
Simplifying (6i)(2i)
Let's apply the above principles to our expression:
(6i)(2i) = 12i²
Now, substitute i² = -1:
12i² = 12(-1) = -12
Therefore, (6i)(2i) = -12.
Conclusion
We successfully simplified the product of the two complex numbers, (6i)(2i), to a real number, -12. This demonstrates how complex numbers can interact and lead to real-valued results.