Answer: |z|=√2, arg=5π/12.
- A |z|=√2, arg=5π/12
- B |z|=√2, arg=7π/12
- C |z|=2, arg=5π/12
- D |z|=1, arg=5π/12
Correct answer: A. |z|=√2, arg=5π/12
Explanation: |z| = |sqrt(3)+i|/|1-i| = 2/sqrt(2) = sqrt(2). arg(numerator) = pi/6; arg(denominator) = -pi/4. arg(z) = pi/6 - (-pi/4) = pi/6 + pi/4 = 2pi/12+3pi/12 = 5pi/12.
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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