Answer: 16.
- A 8
- B 16
- C 16i
- D -16
Correct answer: B. 16
Explanation: 1+i = sqrt(2)(cos(pi/4)+i sin(pi/4)). (1+i)<sup>8</sup> = (sqrt(2))<sup>8</sup> (cos(8*pi/4)+i sin(8*pi/4)) = 16(cos 2pi + i sin 2pi) = 16(1+0) = 16.
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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