What is the argument of the complex number -1 + 0i? (2021)

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Question: What is the argument of the complex number -1 + 0i? (2021)

Options:

Correct Answer: π

Solution:

The argument of -1 + 0i is π (180 degrees) since it lies on the negative x-axis.

What is the argument of the complex number -1 + 0i? (2021)

What is the argument of the complex number -1 + 0i? (2021)

Step 1: Understand that a complex number is in the form a + bi, where a is the real part and b is the imaginary part.
Step 2: Identify the complex number given, which is -1 + 0i. Here, a = -1 and b = 0.
Step 3: Plot the complex number on the complex plane. The real part (-1) is on the x-axis and the imaginary part (0) is on the y-axis.
Step 4: Since the imaginary part is 0, the point lies on the x-axis. Specifically, it is at -1 on the x-axis.
Step 5: Determine the angle (argument) from the positive x-axis to the point -1 + 0i. This angle is measured in radians.
Step 6: The angle from the positive x-axis to the negative x-axis is π radians (or 180 degrees).
Step 7: Conclude that the argument of the complex number -1 + 0i is π.

Complex Numbers – Understanding the representation of complex numbers in the Cartesian plane and their polar form.
Argument of a Complex Number – The angle formed with the positive x-axis, measured in radians or degrees.
Quadrants in the Complex Plane – Knowledge of how complex numbers are positioned in different quadrants and their corresponding angles.