Answer: i.
- A i
- B -i
- C 1
- D -1
Correct answer: A. i
Explanation: i⁻³⁵=1/i³⁵. Find i³⁵: 35=4×8+3, so i³⁵=(i⁴)⁸·i³=1⁸·(-i)=-i. Thus i⁻³⁵=1/(-i). Rationalize: multiply by i/i: i/(-i²)=i/(-(-1))=i/1=i. Answer: i⁻³⁵ = i
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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