Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 122659 by mathocean1 last updated on 18/Nov/20

Determinate the geometric  aspect described by M(z) in  complex plane such that:  arg(z^− −3+i)≡(π/4)[2π]

$${Determinate}\:{the}\:{geometric} \\ $$$${aspect}\:{described}\:{by}\:{M}\left({z}\right)\:{in} \\ $$$${complex}\:{plane}\:{such}\:{that}: \\ $$$${arg}\left(\overset{−} {{z}}−\mathrm{3}+{i}\right)\equiv\frac{\pi}{\mathrm{4}}\left[\mathrm{2}\pi\right] \\ $$

Answered by MJS_new last updated on 18/Nov/20

arg (x) ≡(π/4)[2π] ⇔ x=c+ci  let z=a+bi ⇒ z^− =a−bi  a−bi−3+i=c+ci  ⇒  { ((a−c−3=0 ⇒ c=a−3)),((−b−c+1=0 ⇒ c=1−b)) :}  a−3=1−b ⇒ b=4−a  z=a+(4−a)i  this is a straight line.

$$\mathrm{arg}\:\left({x}\right)\:\equiv\frac{\pi}{\mathrm{4}}\left[\mathrm{2}\pi\right]\:\Leftrightarrow\:{x}={c}+{c}\mathrm{i} \\ $$$$\mathrm{let}\:{z}={a}+{b}\mathrm{i}\:\Rightarrow\:\overset{−} {{z}}={a}−{b}\mathrm{i} \\ $$$${a}−{b}\mathrm{i}−\mathrm{3}+\mathrm{i}={c}+{c}\mathrm{i} \\ $$$$\Rightarrow\:\begin{cases}{{a}−{c}−\mathrm{3}=\mathrm{0}\:\Rightarrow\:{c}={a}−\mathrm{3}}\\{−{b}−{c}+\mathrm{1}=\mathrm{0}\:\Rightarrow\:{c}=\mathrm{1}−{b}}\end{cases} \\ $$$${a}−\mathrm{3}=\mathrm{1}−{b}\:\Rightarrow\:{b}=\mathrm{4}−{a} \\ $$$${z}={a}+\left(\mathrm{4}−{a}\right)\mathrm{i} \\ $$$$\mathrm{this}\:\mathrm{is}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line}. \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com