# 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)#