$If space straight A equals space open square brackets table row cell cos space straight theta end cell cell space space space straight i space sin space straight theta end cell row cell straight i space sin space straight theta end cell cell space space cos space straight theta end cell end table close square brackets comma space then space prove space by space principle space of space mathematical space induction space that straight A to the power of straight n space equals open square brackets table row cell cos space straight theta end cell cell space space space straight i space sin space straight theta end cell row cell straight i space sin space straight theta end cell cell space space cos space straight theta end cell end table close square brackets space where space straight n space element of space straight N.$

Solution

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