(-7%2B5i)(-8-4i).jpeg "(7+3i)(-7+5i)(-8-4i)")
Multiplying Complex Numbers: (7+3i)(-7+5i)(-8-4i)
This article will guide you through multiplying three complex numbers: (7+3i)(-7+5i)(-8-4i). We will break down the process step by step to make it easier to follow.
Step 1: Multiply the first two complex numbers
We start by multiplying the first two complex numbers: (7+3i)(-7+5i).
To do this, we use the distributive property (or FOIL method):
(7+3i)(-7+5i) = (7)(-7) + (7)(5i) + (3i)(-7) + (3i)(5i)
Simplifying:
= -49 + 35i - 21i + 15i²
Remember that i² = -1. Substituting this:
= -49 + 35i - 21i - 15
= -64 + 14i
Step 2: Multiply the result by the third complex number
Now we have (-64 + 14i) and we need to multiply it by (-8-4i):
(-64 + 14i)(-8-4i) = (-64)(-8) + (-64)(-4i) + (14i)(-8) + (14i)(-4i)
Simplifying:
= 512 + 256i - 112i - 56i²
Again, substitute i² = -1:
= 512 + 256i - 112i + 56
= 568 + 144i
Final Result
Therefore, the product of (7+3i)(-7+5i)(-8-4i) is 568 + 144i.