Change the following complex numbers to polar formula 2 (COS π / 4 + isin π / 4) 2 (COS 2 π / 3 + isin 2 π / 3) / 8 (COS π / 4-isin π / 4)

ρ=2*2/8=0.5,θ=π/4+2π/3-(-π/4)=2π=0

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1. In the plane rectangular coordinate system, after translating the line y = - 2x + 1 down four unit lengths, the analytical expression of the line is______ ．
2. In the plane rectangular coordinate system, after translating the line y = - 2x + 3 downward by 2 units, its analytical formula is
3. In the plane rectangular coordinate system, after translating the line y = 2x-1 upward by 4 length units, what is the analytical formula of the line
4. The analytical expression of the straight line obtained by translating the straight line y = - 2x upward by 2 units is______ ．
5. In the plane rectangular coordinate system, given the points a (4,5) and B (4,1), translate the line AB to the right by 5 length units (1) Try to find the area swept by line ab (2) Change the line AB to the broken line ACB, the coordinates of points a and B remain unchanged, C is (2,2), and try to find the area swept by the broken line (3) If the coordinates of points a and B remain unchanged and the coordinates of point C are changed to (1,3), does the area swept by the broken line change? (4) If the coordinates of points a and B remain unchanged and the broken line ACB is changed into a curve, does the area swept by the curve change?
6. In a plane rectangular coordinate system, given points a (- 4,0), B (0,2), now translate line AB to the right, so that a coincides with coordinate 0, then the coordinate of B after translation is___
7. First, the point P (- 2,1) is translated one length unit to the left, and then two length units to the up to get the point P, then the coordinate of P is
8. The analytical expression of the straight line y = 3x + 1 is obtained by translating 2 units to the right and 3 units to the down______ ．
9. The analytic expression of the straight line y = - 3x + 1 is obtained by moving up one unit, and then moving right three units
10. Given that the line y = 3x + 1, translate the line up two units along the y-axis, and then to the right three units, and find the analytical expression of the line after two times of translation
11. Conjugate complex of complex number - I (COS α + isin α)
12. Sin Z + cos z = 0 all solutions Z are complex
13. I hope someone can answer, θ∈ R, z = (a + cos θ) + (2A - sin θ) I If the modulus of complex z = (a + cos θ) + (2A - sin θ) I does not exceed 2 for all θ∈ R, then the value range of real number a is_______ .
14. Why do we set z = cos α + sin β I in some high school plural questions, and if | Z-2 | = 2, why set 2 + cos α + sin α I QAQ, the concept is a little vague,
15. The complex number is known as Z = sin θ + (2-cos ^ 2 θ) I, 0 ≤ θ 1. The complex number is known as Z = sin θ + (2-cos ^ 2 θ) I, 0 ≤ θ
16. If Z is an imaginary number and (Z-2) / (Z & sup2; + 1) belongs to R, find the locus of the point corresponding to Z in the complex plane
17. A sufficient and necessary condition for Z ∈ R is that z = Z conjugate? Right? And a sufficient and necessary condition for Z to be an imaginary number is that Z + Z conjugate belongs to R pair RT
18. Rotate the vector corresponding to the complex z = 2-I 90 degrees counter clockwise, what is the corresponding complex number In addition, tell me the vector corresponding to the complex z = 2-I
19. Is it wrong or correct that the complex number represented by a vector remains unchanged after the translation of the vector? For example, I read a sentence in a book that "no matter where the vector is translated, the complex number it represents is the same". I don't understand it. For example, the complex number represented by the vector (1,1) is 1 + I. after the vector is translated 2 units along the X axis, the complex number it represents should be 3 + I. how can it remain unchanged?
20. If the points corresponding to complex numbers 3 + I and 2 + 3I in the complex plane are p and Q respectively, the complex number corresponding to vector PQ is () A. 5+4iB. 1-2iC. -1+2iD. 1+2i