Lösung 3.1:4a

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In this case, we start by subtracting <math>z</math> from both sides,
In this case, we start by subtracting <math>z</math> from both sides,
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{{Displayed math||<math>z+3i-z=2z-2-z\,\textrm{.}</math>}}
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{{Abgesetzte Formel||<math>z+3i-z=2z-2-z\,\textrm{.}</math>}}
Then we have a <math>z</math> left on the right-hand side,
Then we have a <math>z</math> left on the right-hand side,
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{{Displayed math||<math>3i=z-2\,\textrm{.}</math>}}
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{{Abgesetzte Formel||<math>3i=z-2\,\textrm{.}</math>}}
We add <math>2</math> to both sides to remove the <math>-2</math> from the right hand side,
We add <math>2</math> to both sides to remove the <math>-2</math> from the right hand side,
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{{Displayed math||<math>3i+2=z-2+2\,,</math>}}
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{{Abgesetzte Formel||<math>3i+2=z-2+2\,,</math>}}
and after that we can just read off the solution,
and after that we can just read off the solution,
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{{Displayed math||<math>2+3i=z\,\textrm{.}</math>}}
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{{Abgesetzte Formel||<math>2+3i=z\,\textrm{.}</math>}}
To check that we have calculated correctly, we substitute <math>z=2+3i</math> into the original equation and see that it is satisfied,
To check that we have calculated correctly, we substitute <math>z=2+3i</math> into the original equation and see that it is satisfied,
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{{Displayed math||<math>\begin{align}
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{{Abgesetzte Formel||<math>\begin{align}
\text{LHS} &= z +3i = 2+3i+3i=2+6i\,,\\[5pt]
\text{LHS} &= z +3i = 2+3i+3i=2+6i\,,\\[5pt]
\text{RHS} &= 2z-2 = 2(2+3i)-2 = 4 + 6i -2 = 2+6i\,\textrm{.}
\text{RHS} &= 2z-2 = 2(2+3i)-2 = 4 + 6i -2 = 2+6i\,\textrm{.}
\end{align}</math>}}
\end{align}</math>}}

Version vom 13:06, 10. Mär. 2009

A general strategy when solving equations is to try to get the unknown variable by itself on one side.

In this case, we start by subtracting \displaystyle z from both sides,

\displaystyle z+3i-z=2z-2-z\,\textrm{.}

Then we have a \displaystyle z left on the right-hand side,

\displaystyle 3i=z-2\,\textrm{.}

We add \displaystyle 2 to both sides to remove the \displaystyle -2 from the right hand side,

\displaystyle 3i+2=z-2+2\,,

and after that we can just read off the solution,

\displaystyle 2+3i=z\,\textrm{.}

To check that we have calculated correctly, we substitute \displaystyle z=2+3i into the original equation and see that it is satisfied,

\displaystyle \begin{align}

\text{LHS} &= z +3i = 2+3i+3i=2+6i\,,\\[5pt] \text{RHS} &= 2z-2 = 2(2+3i)-2 = 4 + 6i -2 = 2+6i\,\textrm{.} \end{align}

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_3.1:4a“