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If z = 5 + 12i, find the argument of z. (2020)
If z = 5 + 12i, find the argument of z. (2020)
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Practice Questions
1 question
Q1
If z = 5 + 12i, find the argument of z. (2020)
arctan(12/5)
arctan(5/12)
π/2
0
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The argument of z = 5 + 12i is θ = arctan(12/5).
Questions & Step-by-step Solutions
1 item
Q
Q: If z = 5 + 12i, find the argument of z. (2020)
Solution:
The argument of z = 5 + 12i is θ = arctan(12/5).
Steps: 6
Show Steps
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 θ formed with the positive x-axis in the complex plane.
Step 3: Use the formula for the argument, which is θ = arctan(y/x), where y is the imaginary part and x is the real part of the complex number.
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: θ = arctan(12/5).
Step 6: Calculate the value of arctan(12/5) to find the argument of z.
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