Understanding Multiplying Complex Numbers
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Beginner
Start here! Easy to understand
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Beginner Explanation
Multiply each term of the first complex number by each term of the second using FOIL: $a·c$ (First), $a·di$ (Outer), $bi·c$ (Inner), and $bi·di$ (Last). Then combine like terms and replace $i^2$ with -1 to simplify.
Practice Problems
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1
Quick Quiz
Single Choice Quiz
Beginner
What is the product of $(1 + i)$ and $(1 - i)$?
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2
Real-World Problem
Question Exercise
Intermediate
Teenager Scenario
Imagine you have a complex number $3 + 2i$ representing a vector in a game. Multiply it by $2 + i$ to find the resulting vector.
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3
Thinking Challenge
Thinking Exercise
Intermediate
Think About This
What happens if you multiply a complex number by its conjugate? Consider $a + bi$ and its conjugate $a - bi$.
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4
Challenge Quiz
Single Choice Quiz
Advanced
Calculate the product of $(3 - 4i)$ and $(2 + 5i)$.
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Recap
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