What complex numbers have the same absolute value as #sqrt(3)+i# but subtend a right angle with it at O in the complex plane?
1 Answer
Oct 31, 2016
(2)
Explanation:
Assuming 'O' is
Rotating anticlockwise about
#i(sqrt(3)+i) = isqrt(3)+i^2 = isqrt(3)-1 = -1+isqrt(3)#
Rotating clockwise about
#-i(sqrt(3)+i) = -isqrt(3)-i^2 = -isqrt(3)+1 = 1-isqrt(3)#
So the answer is:
(2)
#" "-1+isqrt(3)" "# or#" "1-isqrt(3)#