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 = 2 5 ((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) .