Question #6d615

1 Answer
May 28, 2016

Answer:

(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#.