（1991•云南）复数z=-3（sin43π-icos43π）的辐角的主值是（）A．43πB．53πC．116πD．π6

Question

（1991•云南）复数z=-3（sin(4)/(3)π-icos(4)/(3)π）的辐角的主值是（　　）

A．(4)/(3)π
B．(5)/(3)π
C．(11)/(6)π
D．(π)/(6)

Answer 1

z＝−3(−sin(π)/(3)+icos(π)/(3))=3(sin(π)/(3)−icos(π)/(3))=3(cos(π)/(6)−isin(π)/(6))=3(cos(11π)/(6)+isin(11π)/(6))．
∴argZ=(11π)/(6)．
故选C．