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Ch. 5 - Complex Numbers, Polar Coordinates and Parametric Equations
Blitzer - Trigonometry 3rd Edition
Blitzer3rd EditionTrigonometryISBN: 9780137316601Not the one you use?Change textbook
All textbooksBlitzer 3rd EditionCh. 5 - Complex Numbers, Polar Coordinates and Parametric EquationsProblem 9
Chapter 5, Problem 9

Plot each complex number and find its absolute value. z = −3 + 4i

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Identify the complex number given: \(z = -3 + 4i\), where the real part is \(-3\) and the imaginary part is \(4\).
Plot the complex number on the complex plane by marking the point with coordinates \(( -3, 4 )\), where the x-axis represents the real part and the y-axis represents the imaginary part.
Recall that the absolute value (or modulus) of a complex number \(z = a + bi\) is given by the formula \(|z| = \sqrt{a^2 + b^2}\).
Substitute the values of \(a = -3\) and \(b = 4\) into the formula to get \(|z| = \sqrt{(-3)^2 + 4^2}\).
Simplify the expression under the square root to find the absolute value, which represents the distance of the point from the origin in the complex plane.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Complex Numbers and the Complex Plane

A complex number is expressed as z = a + bi, where a is the real part and b is the imaginary part. It can be represented as a point (a, b) on the complex plane, with the horizontal axis for the real part and the vertical axis for the imaginary part.
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Plotting Complex Numbers

To plot a complex number, locate its real part on the x-axis and its imaginary part on the y-axis. For z = -3 + 4i, plot the point at (-3, 4) in the complex plane, which visually represents the number.
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Absolute Value (Modulus) of a Complex Number

The absolute value or modulus of a complex number z = a + bi is the distance from the origin to the point (a, b) on the complex plane. It is calculated as |z| = √(a² + b²), representing the magnitude of the complex number.
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Related Practice
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