houssam

Let z = 2e^13πi/6.

Write z, z⁶, z⁴ and z^−2 in the form a + bi.

A norman window has the shape of a rectangle surmounted byasemicircle. (Thus the diameter of the semicircle is equal tothewidth of the rectangle.) If the perimeter of the window is 30ft,find the dimensions of the window so that the greatestpossibleamount of light is admitted.