How to find the complex root of the equation x & # 178; - 2x + 5 = 0,

How to find the complex root of the equation x & # 178; - 2x + 5 = 0,

Let a and B be the two complex roots of the real coefficient equation x ^ 2-2x + a = 0, and find the module of a plus the module of B

Let a and B be the two complex roots of the real coefficient equation x ^ 2-2x + a = 0, and find the module of a plus the module of B
X & sup2; - 2x + a = 0 two complex roots = = > let a = m + in; b = m-in -------- conjugate imaginary roots
A + B = - 2 = = > 2m = - 2 = = > m = - 1 -------- the conjugate imaginary part is eliminated
The + sign in a * b = a = = > M & sup2; + n & sup2; = a -------- real & sup2; + imaginary & sup2; is caused by I & sup2
Modules of a plus modules of B = |a| + |b| = √ (M & sup2; + n & sup2;) + √ (M & sup2; + n & sup2;) = = 2A

Let z = x + Yi (x, y belong to R), (3x-4y) + (3x + 4Y) I be a pure imaginary number, and | Z | = 5, try to find the complex number Z

(3x-4y) + (3x + 4Y) I is a pure imaginary number
So 3x-4y = 0
3x+4y≠0
|z|=5
x²+y²=25
The solution is x = 4, y = 3 or x = - 4, y = - 3
Z = 4 + 3I or Z = - 4 + - 3I