(2-3i).jpeg "(-6-10i)(2-3i)")
Multiplying Complex Numbers: (-6-10i)(2-3i)
This article will demonstrate how to multiply two complex numbers: (-6 - 10i) and (2 - 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.
Multiplication Process
To multiply complex numbers, we follow the same distributive property as with real numbers. We multiply each term in the first complex number by each term in the second complex number:
(-6 - 10i)(2 - 3i) =
(-6 * 2) + (-6 * -3i) + (-10i * 2) + (-10i * -3i)
Simplifying the Expression
Now, we simplify the expression by performing the multiplication and combining like terms:
= -12 + 18i - 20i + 30i²
Since i² = -1, we substitute:
= -12 + 18i - 20i + 30(-1)
Combining real and imaginary terms:
= (-12 - 30) + (18 - 20)i
= -42 - 2i
Final Result
Therefore, the product of (-6 - 10i) and (2 - 3i) is -42 - 2i.