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What is the argument of the complex number z = -1 + 0i?
What is the argument of the complex number z = -1 + 0i?
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Q1
What is the argument of the complex number z = -1 + 0i?
π
0
π/2
-π
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The argument of z = -1 + 0i is arg(z) = π.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the argument of the complex number z = -1 + 0i?
Solution:
The argument of z = -1 + 0i is arg(z) = π.
Steps: 7
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Step 1: Understand that a complex number is in the form z = a + bi, where a is the real part and b is the imaginary part.
Step 2: Identify the real part and the imaginary part of the given complex number z = -1 + 0i. Here, a = -1 and b = 0.
Step 3: The argument of a complex number is the angle it makes with the positive x-axis in the complex plane.
Step 4: Since the imaginary part (b) is 0, the complex number lies on the real axis.
Step 5: Because the real part (a) is negative (-1), the complex number is located on the negative side of the real axis.
Step 6: The angle corresponding to the negative real axis is π radians (or 180 degrees).
Step 7: Therefore, the argument of the complex number z = -1 + 0i is arg(z) = π.
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