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3.1 Übungen

Aus Online Mathematik Brückenkurs 2

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Version vom 08:21, 17. Sep. 2008

       Theory          Exercises      

Exercise 3.1:1

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

a) (52i)+(3+5i) b) 3i(2i)
c) i(2+3i) d) (32i)(7+5i)
e) (1+i)(2i)2 f) i20+i11

Exercise 3.1:2

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

a) 1+i32i b) 3i46i1+i3+2i
c) 1+i3(2i3)2 d) 511+i3i+i23i

Exercise 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).


Exercise 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