# How to Divide Complex Numbers | Summary and Q&A

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January 16, 2020
by
The Math Sorcerer
How to Divide Complex Numbers

## 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 step-by-step 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.

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