In Exercises 1–10, plot each complex number and find its absolute value. z = 3 + 2i

Key Concepts

Complex Numbers

Complex numbers are numbers that have a real part and an imaginary part, expressed in the form z = a + bi, where 'a' is the real part, 'b' is the coefficient of the imaginary unit 'i', and 'i' is defined as the square root of -1. In the given example, z = 3 + 2i, 3 is the real part and 2 is the imaginary part.

Plotting Complex Numbers

Complex numbers can be represented graphically on the complex plane, where the x-axis represents the real part and the y-axis represents the imaginary part. For the complex number z = 3 + 2i, it would be plotted at the point (3, 2) on this plane, allowing for a visual understanding of its position relative to the origin.

Absolute Value of Complex Numbers

The absolute value (or modulus) of a complex number z = a + bi is calculated using the formula |z| = √(a² + b²). This value represents the distance of the point (a, b) from the origin in the complex plane. For z = 3 + 2i, the absolute value would be |z| = √(3² + 2²) = √(9 + 4) = √13.