(7%2B7i)(3%2B3i).jpeg "(2-6i)(7+7i)(3+3i)")
Multiplying Complex Numbers: (2-6i)(7+7i)(3+3i)
This article will walk you through multiplying the complex numbers (2-6i)(7+7i)(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.
Multiplying Complex Numbers
To multiply complex numbers, we use the distributive property (also known as FOIL for binomials). This means we multiply each term in the first complex number by each term in the second complex number.
Calculating the Product
Let's break down the multiplication step by step:
-
Multiply (2-6i)(7+7i):
- (2-6i)(7+7i) = (27) + (27i) + (-6i7) + (-6i7i)
- = 14 + 14i - 42i - 42i^2
- Remember that i^2 = -1, so we can substitute:
- = 14 + 14i - 42i + 42
- = 56 - 28i
-
Multiply the result by (3+3i):
- (56 - 28i)(3+3i) = (563) + (563i) + (-28i3) + (-28i3i)
- = 168 + 168i - 84i - 84i^2
- Substitute i^2 = -1:
- = 168 + 168i - 84i + 84
- = 252 + 84i
Final Result
Therefore, the product of (2-6i)(7+7i)(3+3i) is 252 + 84i.