Question 395841
The angle is in the second quadrant, so {{{sin (theta)}}} is positive. By the Pythagorean identity,


{{{sin^2 (theta) + cos^2 (theta) = 1}}}


{{{sin^2 (theta) + 16/121 = 1}}}


{{{sin^2 (theta) = 105/121}}}


{{{sin (theta) = sqrt(105)/11}}}


Since the cosine corresponds to the x-coordinate or the real part of z, we say that {{{Re(z) = 4/11}}}. Likewise, {{{Im(z) = (sqrt(105)/11)i}}}, so the complex number is {{{z = 4/11 + (sqrt(105)/11)i}}}. Note that we can multiply z by any real constant and the cosine, sine values will still be the same.