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3.3 Übungen

Aus Online Mathematik Brückenkurs 2

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Exercise 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

Answer | Solution a | Solution b | Solution c | Solution d | Solution e

Exercise 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 

Answer | Solution a | Solution b | Solution c | Solution d | Solution e

Exercise 3.3:3

Complete the square of the following expressions

a) z2+2z+3 b) z2+3iz−41
c) −z2−2iz+4z+1 d) iz2+(2+3i)z−1

Answer | Solution a | Solution b | Solution c | Solution d

Exercise 3.3:4

Solve the equations

a) z2=i b) z2−4z+5=0
c) −z2+2z+3=0 d) z1+z=21

Answer | Solution a | Solution b | Solution c | Solution d

Exercise 3.3:5

Solve the equations

a) z2−2(1+i)z+2i−1=0 b) z2−(2−i)z+(3−i)=0
c) z2−(1+3i)z−4+3i=0 d) (4+i)z2+(1−21i)z=17

Answer | Solution a | Solution b | Solution c | Solution d

Exercise 3.3:6

Determine the solution to z2=1+i both in polar form and in the form a+ib, where a and b are real numbers. Use the result to calculate tan8.

Answer | Solution

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