(5-3i)(1%2Bi).jpeg "(4+2i)(5-3i)(1+i)")
Multiplying Complex Numbers: (4+2i)(5-3i)(1+i)
This article will guide you through multiplying the complex numbers (4+2i)(5-3i)(1+i). We will use the distributive property (also known as FOIL) and the fact that i² = -1 to simplify the expression.
Step 1: Multiply the first two complex numbers
Let's begin by multiplying (4+2i) and (5-3i):
(4+2i)(5-3i) = 4(5-3i) + 2i(5-3i)
Distribute: = 20 - 12i + 10i - 6i²
Simplify using i² = -1: = 20 - 2i + 6 = 26 - 2i
Step 2: Multiply the result by the third complex number
Now, we need to multiply (26-2i) by (1+i):
(26-2i)(1+i) = 26(1+i) - 2i(1+i)
Distribute: = 26 + 26i - 2i - 2i²
Simplify using i² = -1: = 26 + 24i + 2 = 28 + 24i
Conclusion
Therefore, the product of (4+2i)(5-3i)(1+i) is 28 + 24i.