What is the argument of the complex number z = -1 + 0i?

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Question: What is the argument of the complex number z = -1 + 0i?

Options:

Correct Answer: π

Solution:

The argument of z = -1 + 0i is arg(z) = π.

What is the argument of the complex number z = -1 + 0i?

What is the argument of the complex number z = -1 + 0i?

Step 1: Understand that a complex number is in the form z = a + bi, where a is the real part and b is the imaginary part.
Step 2: Identify the real part and the imaginary part of the given complex number z = -1 + 0i. Here, a = -1 and b = 0.
Step 3: The argument of a complex number is the angle it makes with the positive x-axis in the complex plane.
Step 4: Since the imaginary part (b) is 0, the complex number lies on the real axis.
Step 5: Because the real part (a) is negative (-1), the complex number is located on the negative side of the real axis.
Step 6: The angle corresponding to the negative real axis is π radians (or 180 degrees).
Step 7: Therefore, the argument of the complex number z = -1 + 0i is arg(z) = π.

Complex Numbers – Understanding the representation of complex numbers in the form a + bi, where a is the real part and b is the imaginary part.
Argument of a Complex Number – The argument of a complex number is the angle formed with the positive real axis in the complex plane, typically measured in radians.
Polar Coordinates – The relationship between rectangular coordinates (a, b) and polar coordinates (r, θ), where r is the modulus and θ is the argument.