Answer: 2.
- A 1
- B 2
- C 3
- D 4
Correct answer: B. 2
Explanation: Compute squares: (1+i)²=1+2i-1=2i and (1-i)²=1-2i-1=-2i. So equation becomes (2i)<sup>n</sup>=(-2i)<sup>n</sup>, i.e., 2<sup>n</sup>·i<sup>n</sup> = 2<sup>n</sup>·(-i)<sup>n</sup>, giving i<sup>n</sup>=(-i)<sup>n</sup>, or (i/(-i))<sup>n</sup>=(-1)<sup>n</sup>=1. Smallest positive n: n=2. Answer: n = 2
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
Read the full Complex Numbers and Quadratic Equations notes →