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Lösung 3.3:3c

Aus Online Mathematik Brückenkurs 2

(Unterschied zwischen Versionen)
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K (Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel))
Zeile 1: Zeile 1:
If we take the minus sign out in front of the whole expression,
If we take the minus sign out in front of the whole expression,
-
{{Displayed math||<math>-\bigl(z^2+2iz-4z-1\bigr)\,,</math>}}
+
{{Abgesetzte Formel||<math>-\bigl(z^2+2iz-4z-1\bigr)\,,</math>}}
and collect together the first-degree terms,
and collect together the first-degree terms,
-
{{Displayed math||<math>-\bigl(z^2+(-4+2i)z-1\bigr)\,,</math>}}
+
{{Abgesetzte Formel||<math>-\bigl(z^2+(-4+2i)z-1\bigr)\,,</math>}}
we can then complete the square of the expression inside the outer bracket,
we can then complete the square of the expression inside the outer bracket,
-
{{Displayed math||<math>\begin{align}
+
{{Abgesetzte Formel||<math>\begin{align}
-\bigl(z^2+(-4+2i)z-1\bigr)
-\bigl(z^2+(-4+2i)z-1\bigr)
&= -\Bigl(\Bigl(z+\frac{-4+2i}{2}\Bigr)^2-\Bigl(\frac{-4+2i}{2}\Bigr)^2-1\Bigr)\\[5pt]
&= -\Bigl(\Bigl(z+\frac{-4+2i}{2}\Bigr)^2-\Bigl(\frac{-4+2i}{2}\Bigr)^2-1\Bigr)\\[5pt]

Version vom 13:12, 10. Mär. 2009

If we take the minus sign out in front of the whole expression,

−z2+2iz−4z−1 

and collect together the first-degree terms,

−z2+(−4+2i)z−1 

we can then complete the square of the expression inside the outer bracket,

−z2+(−4+2i)z−1=−z+2−4+2i2−2−4+2i2−1=−(z−2+i)2−(−2+i)2−1=−(z−2+i)2−(−2)2+4i−i2−1=−(z−2+i)2−4+4i+1−1=−(z−2+i)2−4+4i=−(z−2+i)2+4−4i.
Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_3.3:3c“