Answer: |z|=2, arg=π/6.
- A |z|=2, arg=π/6
- B |z|=2, arg=π/3
- C |z|=√2, arg=π/4
- D |z|=4, arg=π/6
Correct answer: A. |z|=2, arg=π/6
Explanation: |z| = sqrt(3+1) = 2. arg(z) = tan<sup>-1</sup>(1/sqrt(3)) = pi/6.
A complex number z = a+ib is plotted as a point (or vector from the origin) on the Argand plane, with the real part along the horizontal axis and the imaginary part along the vertical; its modulus |z| is the vector's length, and its argument θ is the angle from the positive real axis.
Concept context
Complex numbers in a+ib form, modulus, argument, polar form, cube roots of unity, and quadratic equations with complex roots
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