Project ID:
6000000071
Accepted:
Type:
Layout:
Question:
Match each equation to a figure in which the marked points $x_1$, $x_2$, $x_3$ and $x_4$ correspond to the roots of the equation.
\vspace{-1em}
Questions Title:
Figures
Answers Title:
Equations
Question 1:
{\obrA}
Question 1 Image:
Answer 1:
$x^4+\,\mathrm{i}=0$
Question 2:
{\obrB}
Question 2 Image:
Answer 2:
$x^4+1=0$
Question 3:
{\obrC}
Question 3 Image:
Answer 3:
$x^4-\,\mathrm{i}=0$
Question 4:
{\obrD}
Question 4 Image:
Answer 4:
$x^4-1=0$
Question 5:
{\obrE}
Question 5 Image:
Answer 5:
<p>$x^4+\frac12+\frac{\sqrt3}2\mathrm{i}=0$</p>
Question 6:
{\obrF}
Question 6 Image:
Answer 6:
$x^4+\frac12-\frac{\sqrt3}2\mathrm{i}=0$
Tex:
% tiket 32102
\def\TEXTA{}
\def\TEXTQ{}
\def\preAnswers{\vspace*{-10pt}}
\NastavOD{3}
\def\obrA{\obrMsr[x=2cm,y=2cm]{-1.5}{1.5}{-1.5}{1.5}
{
\coordinate (O) at (0:1);
\coordinate (S) at (0,0);
\coordinate (A) at (67.5:1);
\coordinate (B) at (157.5:1);
\coordinate (C) at (247.5:1);
\coordinate (D) at (337.5:1);
\footnotesize
\obrClip
\obrOsaX
\obrOsaY
\obrPopisX[below right]{1}
\obrPopisX[below left]{-1}
\obrPopisY[above right]{1}
\obrPopisY[below right]{-1}
\draw (1.5,0) node [above left,xshift=3pt]{$Re(x)$};
\draw (0,1.5) node [below right,yshift=3pt]{$Im(x)$};
\draw[dashed] (0,0) circle (1);
\draw[dashed] (A) -- (C);
\draw[dashed] (B) -- (D);
\begin{scope}[thick]
\obrKrizek[2pt]{A}{above right}{x_1}
\obrKrizek[2pt]{B}{above left}{x_2}
\obrKrizek[2pt]{C}{below left}{x_3}
\obrKrizek[2pt]{D}{below right}{x_4}
\end{scope}
\begin{scope}[thick]
\draw[-latex] (0:0.5) arc (0:67.5:0.5);
\obrUhelBZnacka[xshift=5pt, yshift=2pt] {O}{S}{A}{$67.5^{\circ}$}
\end{scope}
\begin{scope}[thick,red]
\draw[-latex] (0:0.6) arc (0:157.5:0.6);
\obrUhelBZnacka[xshift=-13pt, yshift=15pt] {O}{S}{B}{$157.5^{\circ}$}
\end{scope}
\begin{scope}[thick,blue]
\draw[-latex] (0:0.7) arc (0:247.5:0.7);
\obrUhelBZnacka[xshift=-25pt, yshift=-10pt] {O}{S}{C}{$247.5^{\circ}$}
\end{scope}
\begin{scope}[thick,green!60!black]
\draw[-latex] (0:0.8) arc (0:337.5:0.8);
\obrUhelBZnacka[xshift=2pt, yshift=-15pt] {O}{S}{D}{$337.5^{\circ}$}
\end{scope}
}}
\def\obrB{\obrMsr[x=2cm,y=2cm]{-1.5}{1.5}{-1.5}{1.5}
{
\coordinate (O) at (0:1);
\coordinate (S) at (0,0);
\coordinate (A) at (45:1);
\coordinate (B) at (135.5:1);
\coordinate (C) at (225.5:1);
\coordinate (D) at (315:1);
\footnotesize
\obrClip
\obrOsaX
\obrOsaY
\obrPopisX[below right]{1}
\obrPopisX[below left]{-1}
\obrPopisY[above right]{1}
\obrPopisY[below right]{-1}
\draw (1.5,0) node [above left,xshift=3pt]{$Re(x)$};
\draw (0,1.5) node [below right,yshift=3pt]{$Im(x)$};
\draw[dashed] (0,0) circle (1);
\draw[dashed] (A) -- (C);
\draw[dashed] (B) -- (D);
\begin{scope}[thick]
\obrKrizek[2pt]{A}{above right}{x_1}
\obrKrizek[2pt]{B}{above left}{x_2}
\obrKrizek[2pt]{C}{below left}{x_3}
\obrKrizek[2pt]{D}{below right}{x_4}
\end{scope}
\begin{scope}[thick]
\draw[-latex] (0:0.5) arc (0:45:0.5);
\obrUhelBZnacka[xshift=5pt, yshift=2pt] {O}{S}{A}{$45^{\circ}$}
\end{scope}
\begin{scope}[thick,red]
\draw[-latex] (0:0.6) arc (0:135:0.6);
\obrUhelBZnacka[xshift=-11pt, yshift=15pt] {O}{S}{B}{$135^{\circ}$}
\end{scope}
\begin{scope}[thick,blue]
\draw[-latex] (0:0.7) arc (0:225:0.7);
\obrUhelBZnacka[xshift=-25pt, yshift=-6pt] {O}{S}{C}{$225^{\circ}$}
\end{scope}
\begin{scope}[thick,green!60!black]
\draw[-latex] (0:0.8) arc (0:315:0.8);
\obrUhelBZnacka[xshift=-2pt, yshift=-18pt] {O}{S}{D}{$315^{\circ}$}
\end{scope}
}}
\def\obrC{\obrMsr[x=2cm,y=2cm]{-1.5}{1.5}{-1.5}{1.5}
{
\coordinate (O) at (0:1);
\coordinate (S) at (0,0);
\coordinate (A) at (22.5:1);
\coordinate (B) at (112.5:1);
\coordinate (C) at (202.5:1);
\coordinate (D) at (292.5:1);
\footnotesize
\obrClip
\obrOsaX
\obrOsaY
\obrPopisX[below right]{1}
\obrPopisX[below left]{-1}
\obrPopisY[above right]{1}
\obrPopisY[below right]{-1}
\draw (1.5,0) node [above left,xshift=3pt]{$Re(x)$};
\draw (0,1.5) node [below right,yshift=3pt]{$Im(x)$};
\draw[dashed] (0,0) circle (1);
\draw[dashed] (A) -- (C);
\draw[dashed] (B) -- (D);
\begin{scope}[thick]
\obrKrizek[2pt]{A}{above right}{x_1}
\obrKrizek[2pt]{B}{above left}{x_2}
\obrKrizek[2pt]{C}{below left}{x_3}
\obrKrizek[2pt]{D}{below right}{x_4}
\end{scope}
\begin{scope}[thick]
\draw[-latex] (0:0.5) arc (0:22.5:0.5);
\obrUhelBZnacka[xshift=5pt, yshift=-8pt] {O}{S}{A}{$22.5^{\circ}$}
\end{scope}
\begin{scope}[thick,red]
\draw[-latex] (0:0.6) arc (0:112.5:0.6);
\obrUhelBZnacka[xshift=10pt, yshift=8pt] {O}{S}{B}{$112.5^{\circ}$}
\end{scope}
\begin{scope}[thick,blue]
\draw[-latex] (0:0.7) arc (0:202.5:0.7);
\obrUhelBZnacka[xshift=-25pt, yshift=10pt] {O}{S}{C}{$202.5^{\circ}$}
\end{scope}
\begin{scope}[thick,green!60!black]
\draw[-latex] (0:0.8) arc (0:292.5:0.8);
\obrUhelBZnacka[xshift=-25pt, yshift=-18pt] {O}{S}{D}{$292.5^{\circ}$}
\end{scope}
}}
\def\obrD{\obrMsr[x=2cm,y=2cm]{-1.5}{1.5}{-1.5}{1.5}
{
\coordinate (O) at (0:1);
\coordinate (S) at (0,0);
\coordinate (A) at (0:1);
\coordinate (B) at (90:1);
\coordinate (C) at (180:1);
\coordinate (D) at (270:1);
\footnotesize
\obrClip
\obrOsaX
\obrOsaY
\obrPopisX[below right]{1}
\obrPopisX[below left]{-1}
\obrPopisY[above right]{1}
\obrPopisY[below right]{-1}
\draw (1.5,0) node [above left,xshift=3pt]{$Re(x)$};
\draw (0,1.5) node [below right,yshift=3pt]{$Im(x)$};
\draw[dashed] (0,0) circle (1);
\begin{scope}[thick]
\obrKrizek[2pt]{A}{above left}{x_1}
\obrKrizek[2pt]{B}{above left}{x_2}
\obrKrizek[2pt]{C}{above left}{x_3}
\obrKrizek[2pt]{D}{below left}{x_4}
\end{scope}
}}
\def\obrE{\obrMsr[x=2cm,y=2cm]{-1.5}{1.5}{-1.5}{1.5}
{
\coordinate (O) at (0:1);
\coordinate (S) at (0,0);
\coordinate (A) at (60:1);
\coordinate (B) at (150:1);
\coordinate (C) at (240:1);
\coordinate (D) at (330:1);
\footnotesize
\obrClip
\obrOsaX
\obrOsaY
\obrPopisX[below right]{1}
\obrPopisX[below left]{-1}
\obrPopisY[above right]{1}
\obrPopisY[below right]{-1}
\draw (1.5,0) node [above left,xshift=3pt]{$Re(x)$};
\draw (0,1.5) node [below right,yshift=3pt]{$Im(x)$};
\draw[dashed] (0,0) circle (1);
\draw[dashed] (A) -- (C);
\draw[dashed] (B) -- (D);
\begin{scope}[thick]
\obrKrizek[2pt]{A}{above right}{x_1}
\obrKrizek[2pt]{B}{above left}{x_2}
\obrKrizek[2pt]{C}{below left}{x_3}
\obrKrizek[2pt]{D}{below right}{x_4}
\end{scope}
\begin{scope}[thick]
\draw[-latex] (0:0.5) arc (0:60:0.5);
\obrUhelBZnacka[xshift=5pt, yshift=2pt] {O}{S}{A}{$60^{\circ}$}
\end{scope}
\begin{scope}[thick,red]
\draw[-latex] (0:0.6) arc (0:150:0.6);
\obrUhelBZnacka[xshift=-10pt, yshift=12pt] {O}{S}{B}{$150^{\circ}$}
\end{scope}
\begin{scope}[thick,blue]
\draw[-latex] (0:0.7) arc (0:240:0.7);
\obrUhelBZnacka[xshift=-25pt, yshift=-10pt] {O}{S}{C}{$240^{\circ}$}
\end{scope}
\begin{scope}[thick,green!60!black]
\draw[-latex] (0:0.8) arc (0:330:0.8);
\obrUhelBZnacka[xshift=2pt, yshift=-18pt] {O}{S}{D}{$330^{\circ}$}
\end{scope}
}}
\def\obrF{\obrMsr[x=2cm,y=2cm]{-1.5}{1.5}{-1.5}{1.5}
{
\coordinate (O) at (0:1);
\coordinate (S) at (0,0);
\coordinate (A) at (30:1);
\coordinate (B) at (120:1);
\coordinate (C) at (210:1);
\coordinate (D) at (300:1);
\footnotesize
\obrClip
\obrOsaX
\obrOsaY
\obrPopisX[below right]{1}
\obrPopisX[below left]{-1}
\obrPopisY[above right]{1}
\obrPopisY[below right]{-1}
\draw (1.5,0) node [above left,xshift=3pt]{$Re(x)$};
\draw (0,1.5) node [below right,yshift=3pt]{$Im(x)$};
\draw[dashed] (0,0) circle (1);
\draw[dashed] (A) -- (C);
\draw[dashed] (B) -- (D);
\begin{scope}[thick]
\obrKrizek[2pt]{A}{above right}{x_1}
\obrKrizek[2pt]{B}{above left}{x_2}
\obrKrizek[2pt]{C}{below left}{x_3}
\obrKrizek[2pt]{D}{below right}{x_4}
\end{scope}
\begin{scope}[thick]
\draw[-latex] (0:0.5) arc (0:30:0.5);
\obrUhelBZnacka[xshift=5pt, yshift=-8pt] {O}{S}{A}{$30^{\circ}$}
\end{scope}
\begin{scope}[thick,red]
\draw[-latex] (0:0.6) arc (0:120:0.6);
\obrUhelBZnacka[xshift=10pt, yshift=12pt] {O}{S}{B}{$120^{\circ}$}
\end{scope}
\begin{scope}[thick,blue]
\draw[-latex] (0:0.7) arc (0:210:0.7);
\obrUhelBZnacka[xshift=-25pt, yshift=10pt] {O}{S}{C}{$210^{\circ}$}
\end{scope}
\begin{scope}[thick,green!60!black]
\draw[-latex] (0:0.8) arc (0:300:0.8);
\obrUhelBZnacka[xshift=-25pt, yshift=-18pt] {O}{S}{D}{$300^{\circ}$}
\end{scope}
}}