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3.3 Übungen

Aus Online Mathematik Brückenkurs 2

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       Theorie          Übungen      

Übung 3.3:1

Write the following number in the form a+ib, where a and b are real numbers:

a) (i+1)12 b) 21+i312 
c) (43−4i)22  d) 1+i1+i312 
e) (3−i)9(1+i3)(1−i)8

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

Übung 3.3:2

Solve the equations

a) z4=1 b) z3=−1 c) z5=−1−i
d) (z−1)4+4=0 e) z−iz+i2=−1 

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

Übung 3.3:3

Complete the square of the following expressions

a) z2+2z+3 b) z2+3iz−41
c) −z2−2iz+4z+1 d) \displaystyle iz^2+(2+3i)z-1

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

Übung 3.3:4

Solve the equations

a) \displaystyle z^2=i b) \displaystyle z^2-4z+5=0
c) \displaystyle -z^2+2z+3=0 d) \displaystyle \displaystyle\frac{1}{z} + z = \frac{1}{2}

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

Übung 3.3:5

Solve the equations

a) \displaystyle z^2-2(1+i)z+2i-1=0 b) \displaystyle z^2-(2-i)z+(3-i)=0
c) \displaystyle z^2-(1+3i)z-4+3i=0 d) \displaystyle (4+i)z^2+(1-21i)z=17

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

Übung 3.3:6

Determine the solution to \displaystyle \,z^2=1+i\, both in polar form and in the form \displaystyle \,a+ib\,, where \displaystyle \,a\, and \displaystyle \,b\, are real numbers. Use the result to calculate \displaystyle \; \tan \frac{\pi}{8}\,.

Antwort | Lösung

Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/3.3_%C3%9Cbungen“