Answer: 5√3/2 + 5i/2.
- A 5/2 + 5√3i/2
- B 5√3/2 + 5i/2
- C 5 + 5i
- D 5/2 - 5√3i/2
Correct answer: B. 5√3/2 + 5i/2
Explanation: z = r(cos theta + i sin theta) = 5(cos(pi/3)+i sin(pi/3)) = 5(1/2+i(sqrt(3)/2)) = 5/2 + 5sqrt(3)/2 i. So z = 5sqrt(3)/2 + 5i/2 matches option B.
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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