What is the root of the imaginary number I? In the range of complex number, we know that the root of - 1 is I and - I, so what are the root of I and - I? Is there any definition in this respect? If there is, what number field does it belong to?

What is the root of the imaginary number I? In the range of complex number, we know that the root of - 1 is I and - I, so what are the root of I and - I? Is there any definition in this respect? If there is, what number field does it belong to?

The root sign I is: sqrt (2) / 2 + sqrt (2) / 2 * I
The root - I is: sqrt (2) / 2 - sqrt (2) / 2 * I

Can an imaginary number be squared?
What number can be the square number? Is it all plural?

The root sign I is: sqrt (2) / 2 + sqrt (2) / 2 * I
Imaginary numbers are square. All plurals are square

Do imaginary numbers have square roots
How to express the square root of an imaginary number? Can we evaluate it, the root of a higher power?

Yes, the imaginary number is written in triangular form and considered in the complex plane

Square root of imaginary number=

Let this imaginary number be Z1 = m + Ni
Let the square root of the imaginary number be Z2 = a + bi (a, B are real numbers)
Z2^2=Z1
Then a ^ 2-B ^ 2 + 2abi = m + Ni
We get a system of equations
Namely
a^2-b^2=m
2ab=n
The value of solvable A and B
Z2 is the square root of the original imaginary number

The square root of a pure imaginary number is also a pure imaginary number
The square root of a real number is a real number
The square roots of impure imaginary numbers are a pair of conjugate imaginary numbers
The square root of an imaginary number is an imaginary number
Which sentence is right

The square roots of impure imaginary numbers are a pair of conjugate imaginary numbers

If the line y = x + m and the circle x ^ 2 + y ^ 2 + 4x + 2 = 0 have two different common points, then the value range of the real number m is

(0,4)
You can draw a picture to see
The center of the circle is 2 under the radius of (0, - 2)

As shown in the figure, it is known that the center of the small circle is the coordinate origin o, and the radius is 3. The coordinates of the center of the large circle P are (a, 0), and the radius is 5. If ⊙ O and ⊙ P contain, then the value range of the letter A is______ ．

According to the center coordinates of the two circles, the center distance of the circle = | A-0 | = | a |, because when the two circles contain, the center distance of the circle is less than 5-3, that is | a | < 2, the solution is - 2 | a | < 2. So the answer is - 2 | a | < 2

As shown in the figure, there is a uniform magnetic field in the circular region with the origin o as the center and R as the radius,
The magnetic induction intensity is B, and the direction is perpendicular to the xoy plane. There is a light screen parallel to the y-axis at x = 2R, which emits electrons along the positive direction of the y-axis at the origin
If the electron can shoot out of the magnetic field, the range of emission velocity V can be calculated
If the emission velocity v = BER / m, what is the distance from the x-axis to the position where the electron hits the light screen? (expressed by R)
If the electron hits the light screen vertically, what is the emission speed of the electron?

1) If an electron wants to exit the magnetic field, the radius of its trajectory is at least R / 2
R/2=mv/eB,v=ReB/2m
So V & gt; REB / 2m, electrons can be ejected from the magnetic field
2) The trajectory radius can be calculated according to the launching speed
r=mv/eB=R,
As shown in the figure, the exit point Q of the electron, the origin o of the coordinate and the center O of the moving track form an equilateral triangle
According to the geometric relationship, we can calculate that the distance from P point to X axis is √ 3R
3) If you hit the screen vertically, the radius of the electron's trajectory is 2R
2R=mvt/eB
vt=2BeR/m

If the line 3x + 4y-12 = 0 intersects with the x-axis and y-axis at two points a and B respectively, and O is the coordinate origin, then the perimeter of △ OAB is?

First, find the coordinates of the intersection a and B of the line 3x + 4y-12 = 0 and the X and Y axes,
When x = 0, y = 3 B (0,3)
When y = 0, x = 4, a (4,0)
So, OA length is 4, OB length is 3, according to the formula of oblique side length of triangle
If the square of AB = the square of OA + the square of ob, then AB = 5
So the perimeter of triangle OAB is: 3 + 4 + 5 = 12

Given that circle C passes through the intersection of line 2x + y + 4 = 0 and circle x2 + Y2 + 2x-4y + 1 = 0, and the origin is on circle C, then the equation of circle C is______ ．

∵ circle C passes through the intersection of line 2x + y + 4 = 0 & nbsp; and circle x2 + Y2 + 2x-4y + 1 = 0, ∵ let the equation of circle C be x2 + Y2 + 2x-4y + 1 + λ (2x + y + 4) = 0, and ∵ the origin is on circle C, ∵ substitute the coordinates of origin to get 1 + 4 λ = 0, and the solution to get λ = - 14, so the equation of circle C is x2 + Y2 + 2x-4y + 1-14 (2x + y + 4) = 0, and simplify to get x2 + Y2 + 32x − 174y = 0