¿Como se resuelve esto?

Se sabe de la fórmula de Moivre lo que sigue : <img src="https://tex.z-dn.net/?f=%20e%5E%7Bix%7D%3D%5Ccos%20x%2Bi%5Csin%20x%3D%5Ctext%7Bcis%20%7Dx%20%20" />por ello se cumple <img src="https://tex.z-dn.net/?f=%20%5Ctext%7Bcis%20%7Dx%5Ccdot%5Ctext%7Bcis%20%7Dy%3De%5E%7Bix%7D%5Ccdot%20e%5E%7Biy%7D%3De%5E%7B%28x%2By%29i%7D%3D%5Ctext%7Bcis%20%7D%28x%2By%29%20" />Ahora vamos la expresión<img src="https://tex.z-dn.net/?f=%20E%3D%5Cdfrac%7B8%5Ctext%7Bcis%20%7D40%5C%C2%B0%5Ccdot%202%5Ctext%7Bcis%20%7D50%5C%C2%B0%7D%7B4%5Ctext%7Bcis%20%7D15%5C%C2%B0%28-3%5Csqrt2%2B3i%5Csqrt2%29%7D%5C%5C%20%5C%5C%20%5C%5CE%3D%5Cdfrac%7B4%5Ctext%7Bcis%20%7D40%5C%C2%B0%5Ccdot%20%5Ctext%7Bcis%20%7D50%5C%C2%B0%7D%7B%5Ctext%7Bcis%20%7D15%5C%C2%B0%28-3%5Csqrt2%2B3i%5Csqrt2%29%7D%5C%5C%20%5C%5C%20%5C%5CE%3D%5Cdfrac%7B4%5Ctext%7Bcis%20%7D90%5C%C2%B0%7D%7B3%5Ctext%7Bcis%20%7D15%5C%C2%B0%28-%5Csqrt2%2Bi%5Csqrt2%29%7D%5C%5C%20%5C%5C%20%5C%5CE%3D%5Cdfrac%7B4%5Ctext%7Bcis%20%7D90%5C%C2%B0%7D%7B6%5Ctext%7Bcis%20%7D15%5C%C2%B0%5Cleft%28-%5Cdfrac%7B%5Csqrt2%7D%7B2%7D%2Bi%5Cdfrac%7B%5Csqrt2%7D%7B2%7D%5Cright%29%7D%20" /><img src="https://tex.z-dn.net/?f=%20E%3D%5Cdfrac%7B2%5Ctext%7Bcis%20%7D90%5C%C2%B0%7D%7B3%5Ctext%7Bcis%20%7D15%5C%C2%B0%5Ccdot%20%5Ctext%7Bcis%20%7D135%5C%C2%B0%7D%5C%5C%20%5C%5C%20%5C%5C%20E%3D%5Cdfrac%7B2%5Ctext%7Bcis%20%7D90%5C%C2%B0%7D%7B3%5Ctext%7Bcis%20%7D150%5C%C2%B0%7D%5C%5C%20%5C%5C%20%5C%5C%20E%3D%5Cdfrac%7B2%7D%7B3%7D%5Ctext%7Bcis%20%7D%2890%5C%C2%B0-150%5C%C2%B0%29%5C%5C%20%5C%5C%20%5C%5C%20E%3D%5Cdfrac%7B2%7D%7B3%7D%5Ctext%7Bcis%20%7D%28-60%29%5C%5C%20%5C%5C%20%5C%5C%20E%3D%5Cdfrac%7B2%7D%7B3%7D%5Cleft%28%5Cdfrac%7B1%7D%7B2%7D-%5Cdfrac%7B%5Csqrt3%7D%7B2%7Di%5Cright%29%5C%5C%20%5C%5C%20%5C%5C%20%5Cboxed%7BE%3D%5Cdfrac%7B1%7D%7B3%7D-%5Cdfrac%7B%5Csqrt3%7D%7B3%7Di%7D%20" />.