(3-3i).jpeg "(4-2i)(3-3i)")
Multiplying Complex Numbers: (4-2i)(3-3i)
This article will guide you through the process of multiplying two complex numbers: (4-2i)(3-3i).
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 (i² = -1).
Multiplying Complex Numbers
To multiply two complex numbers, we use the distributive property (also known as FOIL - First, Outer, Inner, Last) just like with binomials.
Step 1: Expand the expression
(4-2i)(3-3i) = 4(3-3i) -2i(3-3i)
Step 2: Distribute
= 12 - 12i - 6i + 6i²
Step 3: Simplify using i² = -1
= 12 - 12i - 6i - 6
Step 4: Combine real and imaginary terms
= (12-6) + (-12-6)i
Step 5: Final Result
= 6 - 18i
Therefore, the product of (4-2i) and (3-3i) is 6 - 18i.