Complex Numbers and Modulus

The video tutorial explains how to determine which complex numbers have a modulus of 13. It begins by defining the modulus as the absolute value or distance from the origin in the complex plane. The instructor identifies specific complex numbers with a modulus of 13, such as -13i, and demonstrates how to visualize these numbers by drawing a circle with a radius of 13 centered at the origin. The Pythagorean theorem is used to verify the modulus of other complex numbers, and the concept of complex conjugates is introduced, showing that they share the same modulus. The tutorial concludes by noting that there are infinite points on the circle with a modulus of 13.

What is the modulus of a complex number equivalent to?

• Its argument

• Its real part

• Its imaginary part

• Its absolute value

How can you visualize complex numbers with a specific modulus?

• By drawing a triangle

• By drawing a line

• By drawing a circle

• By drawing a square

Which complex number was identified as having a modulus of 13?

• 0 + 13i

• 13 + 0i

• 13i

• -13i

What theorem is used to verify the modulus of a complex number?

• Fundamental Theorem of Algebra

• Binomial Theorem

• Pythagorean Theorem

• Fermat's Last Theorem

What is the modulus of the complex number 5 + 12i?

• 17

• 13

• 5

• 12

Which of the following is a complex conjugate of -5 + 12i?

• -12 + 5i

• 5 - 12i

• 5 + 12i

• -5 - 12i

What is the modulus of the complex number -5 - 12i?

• 17

• 13

• 12

• 5

Which of the following complex numbers also has a modulus of 13?

• 7 + 10i

• 6 + 8i

• 8 + 9i

• 5 + 12i

What happens to the modulus when you take the complex conjugate of a number?

• It doubles

• It halves

• It remains the same

• It becomes zero

How many complex numbers can have a modulus of 13?

• Infinite

• Four

• Two

• One