Question: The argument of the complex number z = -1 - i is?
Options:
-3π/4
3π/4
π/4
-π/4
Correct Answer: -3π/4
Solution:
The argument of z = -1 - i is θ = tan^(-1)(-1/-1) = -3π/4.
The argument of the complex number z = -1 - i is?
Practice Questions
Q1
The argument of the complex number z = -1 - i is?
-3π/4
3π/4
π/4
-π/4
Questions & Step-by-Step Solutions
The argument of the complex number z = -1 - i is?
Step 1: Identify the complex number z, which is given as z = -1 - i.
Step 2: Recognize that the complex number can be represented in the form z = x + yi, where x = -1 and y = -1.
Step 3: Determine the coordinates of the complex number in the complex plane: (-1, -1).
Step 4: Find the angle θ (argument) using the formula θ = tan^(-1)(y/x). Here, y = -1 and x = -1.
Step 5: Substitute the values into the formula: θ = tan^(-1)(-1/-1) = tan^(-1)(1).
Step 6: The angle for tan^(-1)(1) is π/4, but since both x and y are negative, the angle is in the third quadrant.
Step 7: Adjust the angle for the third quadrant: θ = π + π/4 = 5π/4.
Step 8: Alternatively, you can express the angle as a negative angle: θ = -3π/4, which is equivalent.
Complex Numbers – Understanding the representation of complex numbers in the form z = 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 θ formed with the positive real axis in the complex plane, calculated using the arctangent function.
Quadrants in the Complex Plane – Recognizing the position of complex numbers in different quadrants to determine the correct angle for the argument.
Soulshift Feedback×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy?
