Question

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

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

Answer 1

∵z=

3 +i

(1? 3 i)2

=

3 +i

1?2 3 i?3

=

3 +i

?2?2 3 i

=

( 3 +i)(?2+2 3 i)

(?2?2 3 i)(?2+2 3 i)

=-

3

4

+

1

4

i．
∴

1

z

=

4

? 3 +i

=

4(? 3 ?i)

(? 3 +i)(? 3 ?i)

=?

3

?i
∴|

1

z

|=|?

3

?i|=2
故选项为D