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If z = 2 + 2i, what is the argument of z? (2023)
If z = 2 + 2i, what is the argument of z? (2023)
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Practice Questions
1 question
Q1
If z = 2 + 2i, what is the argument of z? (2023)
π/4
π/2
3π/4
0
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The argument of z is given by tan^(-1)(2/2) = tan^(-1)(1) = π/4.
Questions & Step-by-step Solutions
1 item
Q
Q: If z = 2 + 2i, what is the argument of z? (2023)
Solution:
The argument of z is given by tan^(-1)(2/2) = tan^(-1)(1) = π/4.
Steps: 8
Show Steps
Step 1: Identify the complex number z, which is given as z = 2 + 2i.
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: The real part of z is 2 and the imaginary part is also 2.
Step 4: Use the formula for the argument, which is tan^(-1)(imaginary part / real part).
Step 5: Substitute the values: tan^(-1)(2 / 2).
Step 6: Simplify the fraction: 2 / 2 = 1.
Step 7: Now calculate tan^(-1)(1).
Step 8: The angle whose tangent is 1 is π/4 radians.
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