l2 complex numbers ws
DESCRIPTION
complex numbersTRANSCRIPT
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COMPLEX NUMBERS
1) Find the real and imaginary parts of the following:
a) z = -4+2i b) z = 2i c) z = 5 d) z = 0
Powers of i :
2) Simplify each expression.
a) i562 b) i211 c) i4n+3 , n N d) i16 –i + i1993
3) Find the coefficient of the imaginary part: i20 + 6i1995
4) If P(x) = 4x79 -2x56 +3x15 +2 , find P(i).
5) If f(x) = x20 –x13 -2x22 + 4 , find f(i).
Equality :
6) z1 = 2x +1+3i and z2 = y +(x-2)i , if z1 = z2 find x and y.
7) If 8i3+yi2+5xi+4i8 = 3xi9+2y, find x and y.
8) If x+2y-2i = 5+4xi-3yi, find x.
9) z1 = (2x-3y+1)-(3x-2y-1)i and z2 = (x+y-4)+(x-4y+2)i. If z1 = z2 , find x+y.
Answers1) a) -4,2 b) 0,2 c) 5,0 d) 0,0 2) a) -1 b) -i c) -i d)1 3) -6 4) -7i 5) 7-i 6) 5, 11
7) 4, 4/3 8) 1 9) 9/2
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PAGE 2:
Conjugates:
10) z = -2-5i , find Im( ).
11) (1+i)z =2+i+3i5, find .
12) i +(1+2i) = zi-5 , find z.
13) If z =
14) If , find a+b.
15) If z(3-i) = 1- , find z.
Mixed examples Set 1
16) a) b)
c) d) e)
17) 18) 19)
Answers10) 5 11) 3-i 12) -2-i 13) -11/13 14) 12/5 15) 2/9+i/9
16) a) 7i b) 10i c) -3 d) e) 2 17) 8 18) 19)
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20) 21) (1+i)(1+i3)(1+i6)
22) 23)
24) P(x) = -x6 + 2x5 -3x3 +1 , find P(-i ) .
25) z C, (2-i)z = 1- , find Re(z) and Im(z).
26) P(x,y) = x15 + 2x34y35 + x59y11 – y61 . Find P(i,-i).
27) P (x,y) = 3x17y12 – x12y10 + x3y5 . Find P(-i,i).
28) f(z) = , g(z) = iz , find (fog)(2-i).
29) f(z) = , g(z) = , find (fog)(2+i).
Answers20) -1-i 21) 0 22) 23) i 24) 2-5i 25) ¼,¼ 26) 1-2i 27) -3i 28) 1-i 29) 4+2i
Page 4Mixed examples Set 2
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30) işleminin sonucu kaçtir?
31) olduğuna göre, nedir?
32) eşitliğini sağlayan z karmaşık sayısının gerçel kısmı kaçtır?
33) karmaşık sayısının eşiti kaçtır?
34) olduğuna göre, z karamaşık sayısı nedir?
35) olduğuna göre, a pozitif gerçel sayısı nedir?
36) , olduğuna göre, x aşağıdakilerden hangisi olabilir?
A) -2 B) -1 C) 2 D) 4 E) 5
Answers30) 31) 0 32) 0 33) 34) 8 35) ½ 36) D