Express `(3-i)/(2+i)` in the form `x+iy`, where `x` and `y` are real numbers. (2 marks)
Complex Numbers, EXT2 N1 2021 HSC 11e
The complex numbers `z = 5 + i` and `w = 2 − 4 i` are given.
Find `bar z/{w}`, giving your answer in Cartesian form. (2 marks)
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Complex Numbers, EXT2 N2 2020 SPEC2 5 MC
Given the complex number `z = a + bi`, where `a ∈ R text{\}{0}` and `b ∈ R, \ (4zbarz)/((z + barz)^2)` is equivalent to
- `1 + ((text(Im)(z))/(text(Re)(z)))^2`
- `4[text(Re)(z) xx text(Im)(z)]`
- `4([text(Re)(z)]^2 + [text(Im)(z)]^2)`
- `(2 xx text(Im)(z))/([text(Re)(z)]^2)`
Complex Numbers, EXT1 N1 SM-Bank 5
Let `z = 1 + 2 i` and `w = 3 - i`.
Find, in the form `x + i y`,
- `zw` (1 mark)
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- `overset_((frac{10}{z}))`. (1 mark)
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Complex Numbers, EXT2 N1 2005 HSC 2a
Let `z = 3 + i` and `w=1-i`. Find, in the form `x+iy`,
- `2z+iw` (1 mark)
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- `bar z w` (1 mark)
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- `6/w` (1 mark)
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Complex Numbers, EXT2 N1 2020 HSC 11a
Consider the complex numbers `w = -1 + 4i` and `z = 2 -i`.
- Evaluate `|w|`. (1 mark)
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- Evaluate `w overset_ z`. (2 marks)
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Complex Numbers, EXT2 N1 2019 HSC 11a
Let `z = 1 + 3i` and `w = 2 - i`.
- Find `z + bar w`. (1 mark)
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- Express `z/w` in the form `x + iy`, where `x` and `y` are real numbers. (2 marks)
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Complex Numbers, EXT2 N1 2019 HSC 1 MC
What is the value of `(3 - 2i)^2`?
- `5 - 12i`
- `5 + 12i`
- `13 - 12i`
- `13 + 12i`
Complex Numbers, EXT2 N1 2018 HSC 11a
Let `z = 2 + 3i` and `w = 1 - i.`
- Find `zw`. (1 mark)
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- Express `barz - 2/w` in the form `x + iy`, where `x` and `y` are real numbers. (2 marks)
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Complex Numbers, EXT2 N1 2015 HSC 11a
Express `(4 + 3i)/(2 - i)` in the form `x + iy`, where `x` and `y` are real. (2 marks)
Complex Numbers, EXT2 N1 2012 HSC 1 MC
Let `z = 5 − i` and `w = 2 + 3i`.
What is the value of `2z + barw`?
(A) `12 + i`
(B) `12 + 2i`
(C) `12 − 4i`
(D) `12 − 5i`
Complex Numbers, EXT2 N1 2007 HSC 2a
Let `z = 4 + i` and `w = bar z`. Find, in the form `x + iy`,
- `w` (1 mark)
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- `w - z` (1 mark)
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- `z/w`. (1 mark)
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Complex Numbers, EXT2 N1 2015 HSC 2 MC
What value of `z` satisfies `z^2 = 7 - 24i?`
- `4 - 3i`
- `-4 - 3i`
- `3 - 4i`
- `-3 - 4i`
Complex Numbers, EXT2 N1 2006 HSC 2a
Let `z = 3 + i` and `w = 2 - 5i`. Find, in the form `x + iy`,
- `z^2.` (1 mark)
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- `bar z w.` (1 mark)
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- `w/z.` (1 mark)
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Complex Numbers, EXT2 N1 2009 HSC 2b
Write `(-2 + 3i)/(2 + i)` in the form `a + ib` where `a` and `b` are real. (1 mark)
Complex Numbers, EXT2 N1 2010 HSC 2a
Let `z = 5 − i`.
- Find `z^2` in the form `x + iy`. (1 mark)
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- Find `z + 2barz` in the form `x + iy`. (1 mark)
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- Find `i/z` in the form `x + iy`. (2 marks)
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Complex Numbers, EXT2 N1 2011 HSC 2a
Let `w = 2 - 3i` and `z = 3 + 4i.`
- Find `bar w + z.` (1 mark)
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- Find `|\ w\ |.` (1 mark)
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- Express `w/z` in the form `a + ib`, where `a` and `b` are real numbers. (2 marks)
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Complex Numbers, EXT2 N1 2012 HSC 11a
Express `(2sqrt5 + i)/(sqrt5 − i)` in the form `x + iy`, where `x` and `y` are real. (2 marks)