Question: If z = 1 + i√3, then the argument of z is?
Options:
π/3
π/6
2π/3
5π/6
Correct Answer: π/3
Solution:
The argument θ = tan^(-1)(√3/1) = π/3.
If z = 1 + i√3, then the argument of z is?
Practice Questions
Q1
If z = 1 + i√3, then the argument of z is?
π/3
π/6
2π/3
5π/6
Questions & Step-by-Step Solutions
If z = 1 + i√3, then the argument of z is?
Step 1: Identify the complex number z, which is given as z = 1 + i√3.
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 θ = tan^(-1)(imaginary part / real part).
Step 4: Substitute the values into the formula: θ = tan^(-1)(√3 / 1).
Step 5: Simplify the expression: θ = tan^(-1)(√3).
Step 6: Recall that tan(π/3) = √3, so θ = 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 θ formed with the positive real axis, 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.
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