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If z = 1 + i√3, find the argument of z.
If z = 1 + i√3, find the argument of z.
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Practice Questions
1 question
Q1
If z = 1 + i√3, find the argument of z.
π/3
2π/3
π/6
5π/6
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The argument θ = tan^(-1)(√3/1) = π/3.
Questions & Step-by-step Solutions
1 item
Q
Q: If z = 1 + i√3, find the argument of z.
Solution:
The argument θ = tan^(-1)(√3/1) = π/3.
Steps: 6
Show Steps
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 θ 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.
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