Graphing a Complex Number and Finding Its Absolute Value (8.5.1)

Question 1

• Review: A complex number x + yi has a real part, x, and an imaginary part, y. The imaginary number i represents
the quantity sqrt(-1).

Answer 1

• Review: A complex number x + yi has a real part, x, and an imaginary part, y. The imaginary number i represents
the quantity sqrt(-1).

Question 2

• Complex numbers can be graphed in the complex plane just like points are graphed in the coordinate plane. The horizontal axis of the complex plane measures the real part of the complex number and the vertical axis measures the imaginary part.

Answer 2

• Complex numbers can be graphed in the complex plane just like points are graphed in the coordinate plane. The horizontal axis of the complex plane measures the real part of the complex number and the vertical axis measures the imaginary part.

Question 3

• The absolute value or modulus of a complex number z = x + yi is denoted |z|. It represents the distance of z from the origin in the complex plane. Calculate it using the Pythagorean theorem: |z| = |x + yi| = sqrt(x^2 + y^2).

Answer 3

• The absolute value or modulus of a complex number z = x + yi is denoted |z|. It represents the distance of z from the origin in the complex plane. Calculate it using the Pythagorean theorem: |z| = |x + yi| = sqrt(x^2 + y^2).