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Complex Numbers, SPEC2 2011 VCAA 5 MC

A certain complex number `z`, where `|\ z\ | > 1`, is represented by the point on the following argand diagram.
 

SPEC2 2011 VCAA 5 MC
 

All axes below have the same scale as those in the diagram above.

The complex number  `1/barz`  is best represented by

SPEC2 2011 VCAA 5 MC ab

SPEC2 2011 VCAA 5 MC cd

SPEC2 2011 VCAA 5 MC e

Show Answers Only

`C`

Show Worked Solution

`|z| > 1`

`|1/(barz)| < 1`

`1/(barz)` `= 1/(x – iy) xx (x + iy)/(x + iy)`
  `= (x + iy)/(x^2 + y^2)`
  `= z/(|z|^2)`

 
`:.\ 1/barz\ \ text(has same argument as)\ z,\ text(smaller magnitude.)`

`=> C`