How to Divide Complex Numbers  Summary and Q&A
TL;DR
Learn how to divide complex numbers by multiplying them with their conjugate and simplifying.
Key Insights
 🗂️ Dividing complex numbers involves multiplying by the conjugate of the denominator.
 ➗ Distributing and simplifying the numerator is an important step in the division process.
 ✖️ Understanding the formula for multiplying a complex number with its conjugate can help simplify the denominator.
 😑 Dividing complex numbers requires simplifying both the real and imaginary parts of the expression.
 😑 Dividing by the greatest common divisor helps in simplifying the resulting expression.
 🗂️ Dividing complex numbers can be done by following a stepbystep procedure.
 🤘 The conjugate of a complex number is formed by changing the sign of the imaginary part.
Transcript
hey what's up everyone so in this video we're going to divide complex numbers so we have 6 plus 2i over 5 minus 3i and so the way to do this is to always look at the bottom piece and multiply by the conjugate in a clever way so because the bottom piece is 5 minus 3i we have to multiply by 5 plus 3i like this and then you divide by the same thing ri... Read More
Questions & Answers
Q: How do you divide complex numbers?
To divide complex numbers, you multiply the numerator and denominator by the conjugate of the denominator, then simplify the resulting expression.
Q: Why do we multiply by the conjugate?
Multiplying by the conjugate eliminates the imaginary terms in the denominator, making it easier to simplify and calculate the division.
Q: What is the formula for multiplying a complex number and its conjugate?
The formula for multiplying a complex number, such as (a  bi), with its conjugate, (a + bi), is (a^2 + b^2).
Q: How do you simplify the resulting expression?
To simplify the expression, divide both the real and imaginary parts by their greatest common divisor.
Summary & Key Takeaways

Dividing complex numbers involves multiplying by the conjugate of the denominator.

Distribute and simplify the numerator, and use the formula for multiplying a complex number with its conjugate for the denominator.

Simplify the resulting expression by dividing both the real and imaginary parts by their greatest common divisor.