Maths Ext 2 Complex Numbers and Polynomials Qs (1 Viewer)

mreditor16 · Jul 10, 2016

Heya everyone!

Here is a compilation of a few questions which cover Polynomials and Complex Numbers. No answers are provided, so feel free to help each other out with any questions that trouble you.

Here is the link to the questions on Complex Numbers --> https://www.dropbox.com/s/r9pgzw1bbd09beh/4U Complex Numbers Revision Sheet.docx?dl=0

Here is the link to the questions on Polynomials --> https://www.dropbox.com/s/37uw946szxan0u5/4U Polynomials Revision Sheet.docx?dl=0

Cheers!

aoc · Jul 14, 2016

for the locus question in the complex numbers (Q4) i got that the exclusion is x^2+y^2 cant = 0, can this exclusion be simplified?

InteGrand · Jul 14, 2016

aoc said:
for the locus question in the complex numbers (Q4) i got that the exclusion is x^2+y^2 cant = 0, can this exclusion be simplified?

$\noindent Yes $\textendash$ that exclusion just says that $z\neq 0$, which is clear because $z$ is on the denominator of the given expression.$

aoc · Jul 14, 2016

so would i write z cant = 0 or x^2+y^2 cant = 0 (also why does the latter mean z cant =0)

leehuan · Jul 14, 2016

aoc said:
so would i write z cant = 0 or x^2+y^2 cant = 0 (also why does the latter mean z cant =0)

$z\neq 0$

$\text{Writing }x^2+y^2\neq 0\text{ isn't technically wrong however is lacking clarity. The reason why it works is that keep in mind }x\text{ and }y\text{ are }\textbf{REAL}.\\ \text{When you square a real number, it has to be positive or equal to 0. So if you add two of them together, the both had to be 0, i.e. }x=y=0.\text{ This means }z=x+iy=0+0i=0$

$\text{Alternatively, }x^2+y^2=|z|^2=0 \iff z=0$

mreditor16 · Jul 14, 2016

InteGrand said:
$\noindent Yes $\textendash$ that exclusion just says that $z\neq 0$, which is clear because $z$ is on the denominator of the given expression.$

leehuan said:
$z\neq 0$

$\text{Writing }x^2+y^2\neq 0\text{ isn't technically wrong however is lacking clarity. The reason why it works is that keep in mind }x\text{ and }y\text{ are }\textbf{REAL}.\\ \text{When you square a real number, it has to be positive or equal to 0. So if you add two of them together, the both had to be 0, i.e. }x=y=0.\text{ This means }z=x+iy=0+0i=0$

$\text{Alternatively, }x^2+y^2=|z|^2=0 \iff z=0$

Basically, what Integrand and leeuhan said, aoc (Y)

mreditor16 · Jul 20, 2016

Maths Ext 2 Complex Numbers and Polynomials Qs (1 Viewer)

mreditor16

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aoc

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InteGrand

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aoc

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leehuan

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mreditor16

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mreditor16

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