How can z = a * cost + IB * Sint (a, B are real constants) be expressed as a rectangular coordinate equation? By the way, let me talk about the relationship between complex equation and rectangular equation

In contrast, the complex equation of x = acost, y = bsint is introduced to calculate the complex number, which has no real significance

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1. If the complex sequence {an} satisfies A1 = 0, an = (an-1) ^ 2 + I (n is greater than or equal to 2), then the sum of its first 2007 terms is?
2. It is proved that the polynomial A0 * x ^ n + A1 * x ^ n-1 + A2 * x ^ n-2 +. +... An = 0 has at least one real root when n is odd. (A0! = 0)
3. Let A0 + A1 / 2 +. + an / (n + 1) = 0, and prove that the polynomial f (x) = A0 + a1x +. + anx ^ n has at least one zero point in (0,1)
4. Should the plural be z = a + bi or Z = a + IB I saw z = a + bi in my high school math textbook But the advanced mathematics book says z = a + IB Which one is right
5. Given that a, B and C are the three roots of the equation x ^ 3 + PX + q = 0, how to get a + B + C = 0 according to the relationship between the root and the coefficient Such as the title
6. How to prove that an equation of degree n of one variable must have complex roots
7. What is the sum of n roots of the equation of degree n in one variable? Can there be a proof process/ One variable n-th path The sum of n roots of XN + an-1xn-1 + ····· + a1x + A0 = 0 is equal to?
8. What is the relationship between the root and the coefficient of the equation of degree n of one variable Quadratic equation of one variable Univariate cubic equation . What does it have to do with coefficient
9. Write out a quadratic equation with one variable, so that one root is greater than 1, the other root is less than 1, and the equation with quadratic coefficient of 1 is______ ．
10. Write out a quadratic equation of one variable with one root of 2 and the other root of 1
11. A mathematical problem on the complex number! If the complex number Z1 satisfies Z1 = I (2-z1) (I is an imaginary unit), if | Z | = 1, find the maximum value of | z-z1 |
12. Let the vertices of a polygon be in the form of 1 + Z + Z2 +..., in the complex plane +The point of ZK-1 and; where | Z|
13. Mathematical problem solving, complex number Given z = (2m square + 3m-2) + (m square + m-2) I (M belongs to R) When z = 0, find the value of M
14. In the range of complex number, the square of a number is equal to the conjugate complex number of the number. How many such numbers are written separately
15. The conjugate complex of complex number 2 + i1-2i is______ ．
16. Given the complex number Z = 2 − 2i1 + I, then the conjugate complex number of Z is equal to () A. 2iB. -2iC. iD. -i
17. If the conjugate complex number of Z + Z = 4 and the conjugate complex number of Z * z = 8, then the conjugate complex number of Z / Z is equal to? Detailed point answer, thank you
18. If the complex number Z is on the circle | Z | = 2, then it is proved that: | 1 / (Z ^ 4-4z ^ 2 + 3)|
19. If the complex z = (m-1) / 3 - (m-2) I (m ∈ R), its corresponding point on the complex plane is Z, then the shortest distance from point (1,2) on the complex plane to point Z is? The answer is = 2 √ 10 / 5
20. Given | x + Yi | = 2 (x, y ∈ R), in the complex plane, find the set of points representing complex x + Yi Seek detailed process