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3.1 Übungen

Aus Online Mathematik Brückenkurs 2

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Version vom 13:43, 10. Mär. 2009

Theorie

Übungen

Übung 3.1:1

Write in the form a+bi, where a and b are real numbers

a)	(5−2i)+(3+5i)	b)	3i−(2−i)
c)	i(2+3i)	d)	(3−2i)(7+5i)
e)	(1+i)(2−i)2	f)	i20+i11

Übung 3.1:2

Write in the form a+bi, where a and b are real numbers,

a)	1+i3−2i	b)	3i4−6i−1+i3+2i
c)	1+i3(2−i3)2	d)	5−11+i3i+i2−3i

Antwort | Lösung a | Lösung b | Lösung c | Lösung d

Übung 3.1:3

Determine the real number \displaystyle \,a\, such that the expression \displaystyle \ \displaystyle\frac{3+i}{2+ai}\ becomes purely imaginary (i.e. the real part equals zero).

Antwort | Lösung

Übung 3.1:4

Solve the equations

a)	\displaystyle z+3i=2z-2	b)	\displaystyle (2-i) z= 3+2i
c)	\displaystyle iz+2= 2z-3	d)	\displaystyle (2+i) \overline{z} = 1+i
e)	\displaystyle \displaystyle\frac{iz+1}{z+i} = 3+i	f)	\displaystyle (1+i)\overline{z}+iz = 3+5i

Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/3.1_%C3%9Cbungen“

1. Differentialrechnung

2. Integralrechnung

3. Komplexe Zahlen