If z = 5 + 12i, find the argument of z. (2020)

₹0.0

Question: If z = 5 + 12i, find the argument of z. (2020)

Options:

Correct Answer: arctan(12/5)

Exam Year: 2020

Solution:

The argument of z = 5 + 12i is θ = arctan(12/5).

If z = 5 + 12i, find the argument of z. (2020)

If z = 5 + 12i, find the argument of z. (2020)

Step 1: Identify the complex number z, which is given as z = 5 + 12i.
Step 2: Recognize that the argument of a complex number is the angle θ formed with the positive x-axis in the complex plane.
Step 3: Use the formula for the argument, which is θ = arctan(y/x), where y is the imaginary part and x is the real part of the complex number.
Step 4: In this case, the real part (x) is 5 and the imaginary part (y) is 12.
Step 5: Substitute the values into the formula: θ = arctan(12/5).
Step 6: Calculate the value of arctan(12/5) to find the argument of z.

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 θ formed with the positive real axis, calculated using the arctangent of the ratio of the imaginary part to the real part.
Trigonometric Functions – Knowledge of how to use the arctangent function to find angles in right triangles.