If z = 5 + 12i, what is the argument of z? (2022)

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Question: If z = 5 + 12i, what is the argument of z? (2022)

Options:

Correct Answer: arctan(12/5)

Solution:

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

If z = 5 + 12i, what is the argument of z? (2022)

If z = 5 + 12i, what is the argument of z? (2022)

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 it makes with the positive x-axis in the complex plane.
Step 3: Use the formula for the argument, which is arctan(y/x), where y is the imaginary part and x is the real part.
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: 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 formed with the positive real axis in the complex plane, 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 based on the ratio of sides in a right triangle.