Project ID:
5000000016
Accepted:
Template:
Question:
V sústave súradníc sú znázornené komplexné čísla \( A \)-\( J \). Vypočítajte dané operácie s nimi a označte správny výsledok.
Question Row 1:
${\color{cyan}A}+B$
Answer Row 1:
*$5-6\mathrm{i}$, $-6+5\mathrm{i}$, $-1$, $-\mathrm{i}$
Question Row 2:
${\color{green!60!black}D}-{\color{yellow!80!black}C}$
Answer Row 2:
*$5+6\mathrm{i}$, $5+2\mathrm{i}$, $-1+6\mathrm{i}$, $-1+2\mathrm{i}$
Question Row 3:
${\color{orange}E}\cdot{\color{blue}G}$
Answer Row 3:
*$-12+5\mathrm{i}$, $12+5\mathrm{i}$, $-2+11\mathrm{i}$, $-12$
Question Row 4:
${\color{purple}I}/{\color{magenta}H}$
Answer Row 4:
*$-\frac35-\frac45\mathrm{i}$, $-\frac35+\frac45\mathrm{i}$, $\frac35-\frac45\mathrm{i}$, $\frac35+\frac45\mathrm{i}$
Question Row 5:
${\color{gray}F}^5$
Answer Row 5:
*$128-128\mathrm{i}$, $128+128\mathrm{i}$, $-128-128\mathrm{i}$, $-128+128\mathrm{i}$
Question Row 6:
$\sqrt{\color{red}J}$
Answer Row 6:
*$\pm\mathrm{i}$, $\pm1$, $\{-1;\mathrm{i}\}$, $\{-1;-\mathrm{i}\}$
Tex:
% http://math4u.vsb.cz/ticket/32101
\let\oldQuestion\Question
\def\I{\mathrm{i}}
\def\Question{
\begin{minipage}[t]{0.6\linewidth}
\leavevmode
\oldQuestion
\end{minipage}
\hfill
\begin{minipage}[t]{0.35\linewidth}
\leavevmode
\kern -30pt
\def\delka{0.35cm}
\obrMsr[x=\delka,y=\delka]{-5}8{-5}7
{
\coordinate (A) at (3,-2);
\coordinate (B) at (2,-4);
\coordinate (C) at (-3,-2);
\coordinate (D) at (2,4);
\coordinate (E) at (-2,3);
\coordinate (F) at (-2,2);
\coordinate (G) at (3,2);
\coordinate (H) at (1,-3);
\coordinate (I) at (-3,1);
\coordinate (J) at (-1,0);
\obrClip
\draw[gray!30,step=1] (-5,-5) grid (5,5);
\draw[->] (-5,0) -- (5,0) node [right]{\small{$\mathrm{Re}(z)$}};
\draw[->] (0,-5) -- (0,5) node [above]{\small{$\mathrm{Im}(z)$}};
\obrPopisX[below]{-4,-2,2,4}
\obrPopisY[left]{-4,-2,2,4}
\begin{scope}[cyan]
\obrKrizek[2pt]{A}{right}{A}
\end{scope}
\begin{scope}[black]
\obrKrizek[2pt]{B}{above right}{B}
\end{scope}
\begin{scope}[yellow!80!black]
\obrKrizek[2pt]{C}{below left}{C}
\end{scope}
\begin{scope}[green!60!black]
\obrKrizek[2pt]{D}{above right}{D}
\end{scope}
\begin{scope}[orange]
\obrKrizek[2pt]{E}{above}{E}
\end{scope}
\begin{scope}[gray]
\obrKrizek[2pt]{F}{below}{F}
\end{scope}
\begin{scope}[blue]
\obrKrizek[2pt]{G}{above right}{G}
\end{scope}
\begin{scope}[magenta]
\obrKrizek[2pt]{H}{above right}{H}
\end{scope}
\begin{scope}[purple!80!black]
\obrKrizek[2pt]{I}{left}{I}
\end{scope}
\begin{scope}[red]
\obrKrizek[2pt]{J}{below right,xshift=-2pt}{J}
\end{scope}
}
\end{minipage}
}
\pocetsloupcu{4}