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
I don't quite understand that if Z is an imaginary number, it is AI. (Z-2) / (Z & sup2; + 1) = (AI-2) / ((AI) ^ 2 + 1) = (AI-2) / (1-A ^ 2) if he belongs to R, a should not be equal to 0, so what's the trajectory? If Z is a complex number, it's OK to go on
RELATED INFORMATIONS
- 1. 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
- 2. 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,
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- 12. 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
- 13. 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?
- 14. 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
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