JEE Main 1998 Mathematics question on Complex Numbers and Quadratic Equations
The value of ∑k=16(sin72πk−icos72πk) is
A.
−1
B.
0
C.
−i
D.
i
Show answer and solution
Correct option: D
Solution
Each term can be written as -i(cos(2πk/7) + i·sin(2πk/7)) = -i·e^(i·2πk/7). So the sum equals -i · Σ(k=1 to 6) e^(i·2πk/7). The values e^(i·2πk/7) for k=0,1,...,6 are all 7th roots of unity, whose sum is 0. Therefore Σ(k=1 to 6) e^(i·2πk/7) = 0 - e0 = -1. The full sum equals -i·(-1) = i.
[1998]
Practise Complex Numbers and Quadratic Equations the way it is asked
A timed set of real JEE Main Complex Numbers and Quadratic Equations questions, graded as the exam grades. No sign-up.
