Question

Question #6d615

Answer 1

(2) 4

Explanation:

The numbers `0`, `1` and `1+sin(pi/8)+icos(pi/8)` form an isoceles triangle with largest angle `(5pi)/8` and smaller angles each `(3pi)/16`.

The Complex conjugate `1+sin(pi/8)-icos(pi/8)` forms a similar isoceles triangle with `0` and `1`.

So the quotient forms an angle `(3pi)/8` with the Real axis.

Note that, though we are not really interested in the modulus, it will be `1` since we are dividing a number by its Complex conjugate.

So the quotient is actually `cos ((3pi)/8) + i sin ((3pi)/8)`

The smallest integer multiplier that makes this angle into an odd multiple of `pi/2` is `4`, giving `(3pi)/2`, hence the answer is number (2) `4`

The actual value will be `-i`.