Answer: 4i.
- A 2i
- B 4
- C 2+2i
- D 4i
Correct answer: D. 4i
Explanation: De Moivre's theorem: z=|z|(cosθ+i sinθ)=2(cos π/4+i sin π/4). Then z²=|z|²(cos 2θ+i sin 2θ)=4(cos π/2+i sin π/2)=4(0+i·1)=4i. So |z²|=4, arg(z²)=π/2. Answer: z² = 4i
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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