If z = 1 + √3i, what is the argument of z? (2015)

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Question: If z = 1 + √3i, what is the argument of z? (2015)

Options:

Correct Answer: π/3

Exam Year: 2015

Solution:

The argument is given by tan^(-1)(√3/1) = π/3.

If z = 1 + √3i, what is the argument of z? (2015)

If z = 1 + √3i, what is the argument of z? (2015)

Step 1: Identify the complex number z, which is given as z = 1 + √3i.
Step 2: Recognize that the real part of z is 1 and the imaginary part is √3.
Step 3: Use the formula for the argument of a complex number, which is given by the tangent function: argument = tan^(-1)(imaginary part / real part).
Step 4: Substitute the values into the formula: argument = tan^(-1)(√3 / 1).
Step 5: Simplify the expression: argument = tan^(-1)(√3).
Step 6: Recall that tan(π/3) = √3, so the argument is π/3.

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 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 – Using trigonometric functions, specifically the tangent function, to find the angle corresponding to a given ratio.