Question

Maths class 11th


Q. Find the value of
i^k +i^(k+1) +i^(k+2) + i^(k+3)​

Answer 1

Answer:

ANSWER

Let A(3k−1,k−2), B(k,k−7) and C(k−1,−k−2)

If the point are collinear then

Slope of AB= slope of BC ...(1)

Slope of AB=

k−(3k−1)

k−7−(k−2)

Slope of BC=

(k−1)−k

(−k−2)−(k−7)

from (1) we should have

k−3k+1

k−7−k+2

=

k−1−k

−k−2−k+7

−5k+1

−5

=

−1

−2k+5

⇒(−2k+5)(−2k+1)=5

⇒4k∗2−12k+5=5

⇒4k(k−3)=0

for k=0 and k=3 points are collinear.

Answered By