已知复数Z=3+i(1-3i)2，则|z|=（）A．14B．12C．1D．2

Question

已知复数Z= (3+i)/((1-3i)2) ，则|z|=（　　）

A． (1)/(4)

B． (1)/(2)

C．1

D．2

Answer 1

化简得Z= (3+i)/((1-3i )2) = (3+i)/(-2-23i) = -(1)/(2) • (3+i)/(1+3i)
= -(1)/(2) • ((3+i)(1-3i))/((1+3i)(1-3i)) = -(1)/(2) • (23-2i)/(4) = -(3)/(4) +(i)/(4) ，
故|z|=

(-(3)/(4) ) 2 +((1)/(4) ) 2

= (1)/(2) ，
故选B