设复数z＝(1−3i)5，求z的模和辐角的主值．

Question

设复数z＝(1−√(3)i)5，求z的模和辐角的主值．

Answer 1

∵(1−√(3)i)5＝25((1)/(2)−(√(3))/(2)i)5＝32(cos(5)/(3)π+isin(5)/(3)π)5＝32(cos(25)/(3)π+isin(25)/(3)π)
=32(cos(π)/(3)+isin(π)/(3))
∴复数z的模为32，的模和辐角的主值为(π)/(3).