The diagram shows the complex number `z` on the Argand diagram.
Which of the following diagrams best shows the position of `frac{z^2}{|z|}`?
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Complex Numbers, EXT2 N1 2016 HSC 4 MC
The Argand diagram shows the complex numbers `z` and `w`, where `z` lies in the first quadrant and `w` lies in the second quadrant.
Which complex number could lie in the 3rd quadrant?
- `-w`
- `2 iz`
- `bar z`
- `w - z`
Show Worked Solution
`text(Using the parallelogram method:)`
`text(From the graph above,)`
`w – z\ \ text(could lie in 3rd quadrant.)`
`=> D`
Complex Numbers, EXT2 N1 2012 HSC 3 MC
The complex number `z` is shown on the Argand diagram below.
Which of the following best represents `i barz`?
Show Worked Solution
`ibarz\ text(is)\ bar z\ text(rotated)\ 90^@\ text(anticlockwise.)`
`=>A`
Complex Numbers, EXT2 N1 2014 HSC 8 MC
The Argand diagram shows the complex numbers `w`, `z` and `u`, where `w` lies in the first quadrant, `z` lies in the second quadrant and `u` lies on the negative real axis.
Which statement could be true?
- `u = zw` and `u = z + w`
- `u = zw` and `u = z − w`
- `z = uw` and `u = z + w`
- `z = uw` and `u = z − w`
Show Worked Solution
`text(Using the parallelogram method, it could be true that)`
`u = z − w`
`=>\ text{Eliminate (A) and (C)}`
| `text{arg}(u)` | `=\ text{arg}(w) + text{arg}(z)` |
| `u` | ` = zw` |
`=> B`
Complex Numbers, EXT2 N1 2009 HSC 2c
The points `P` and `Q` on the Argand diagram represent the complex numbers `z` and `w` respectively.
Copy the diagram into your writing booklet, and mark on it the following points:
- the point `R` representing `iz.` (1 mark)
- the point `S` representing `bar w.` (1 mark)
- the point `T` representing `z + w.` (1 mark)
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Show Answers Only
i, ii, and iii.
Show Worked Solution
i, ii, and iii.