The Absolute Value of a Complex Number | Summary and Q&A

TL;DR

The absolute value (modulus) of a complex number represents its distance from the origin in the complex plane.

Key Insights

• ✈️ The absolute value (modulus) of a complex number is analogous to the distance from the origin in the complex plane.
• 🫚 Modulus can be computed using the formula square root of (a^2 + b^2).
• #️⃣ Modulus allows for comparison between complex numbers, unlike the numbers themselves.
• #️⃣ Every real number is a complex number with an imaginary part of 0.

Transcript

hello in this video we're going to discuss something known as the absolute value of a complex number so a more common word other than absolute value for what we're going to discuss is modulus so more often than not people call this the modulus of a complex number so what is it let me show you so by a complex number I mean a number which I'll call Z... Read More

Questions & Answers

Q: What is a complex number and how is it represented?

A complex number consists of a real part (a) and an imaginary part (b) and is written as a+bi.

Q: How is the modulus of a complex number defined?

The modulus of a complex number is the distance between the number and the origin in the complex plane.

Q: What is the formula for finding the modulus of a complex number?

The formula is the square root of the sum of the squares of the real part (a) and the imaginary part (b).

Q: Can the modulus of complex numbers be used for comparison?

Yes, if the modulus of a complex number Z1 is smaller than the modulus of Z2, Z1 is closer to the origin in the complex plane.

Q: What happens if the moduli of two complex numbers are equal?

If the moduli are equal, the complex numbers lie on the same circle with the origin as the center.

Summary & Key Takeaways

• A complex number is represented as a+bi, where a is the real part and b is the imaginary part.

• The modulus of a complex number is the distance between the number and the origin in the complex plane.

• The formula for finding the modulus of a complex number is the square root of a squared plus b squared.