X = - I is a solution of the equation x ^ 2 + 1 = 0 in the complex set C?

X = - I is a solution of the equation x ^ 2 + 1 = 0 in the complex set C?

yes.
（-i)²+1=-1+1=0

How to solve complex equation?
Z^2-3iZ-(3-i)=0
The answer in the book is Z = 1 + I, - 1 + 2I

Because of the formula IZ,
It's not easy to find if it's in exponential form,
Let it be in triangular form, three quantities should be solved simultaneously,
So let z = a + bi
So (a ^ 2-B ^ 2) + 2abi - 3AI + 3B - 3 + I = 0
That is, (a ^ 2-B ^ 2 + 3b-3) + (2ab-3a + 1) I = 0
a^2-b^2+3b-3=0 …… ①
And 2ab-3a + 1 = 0 ②
From ② B = (3a - 1) / 2A = 3 / 2 - 1 / 2A ③
Substituting (3) into (1) yields a ^ 2 - 1 / 4A ^ 2 = 3 / 4
That is 4A ^ 4 - 3A ^ 2-1 = 0
The solution of a ^ 2 = 1 or - 1 / 4 is obtained by substitution method ④
Therefore, it can be concluded from (3) and (4)
a1=1,b1=1,z1= 1+ i
a2=-1,b2=2,z2= -1+2i
PS
And how do you solve the complex equation?
I did it in several ways,
PPS
The following is an introduction to the exponential form (Euler's theorem in functions of complex variables)
I have to say that "God's formula" is really a wonderful formula
So is Euler's theorem

Let a, B and C be odd numbers, and prove that the equation AX ^ 2 + BX + C = 0 has no rational root
Such as the title~~~~~~~~~
Er ~ ~ I will prove the problem of integer. How to prove that there is no rational root

According to Weida's theorem
x1+x2=-a/b
x1x2=c/a
Because a, B, C are all odd numbers
So C / A is odd
X1x2 is odd
Because only the odd and the odd multiply to get the odd
So X1 and X2 are odd numbers, respectively
X1 + x2 are even numbers
But because a, B, C are all odd numbers
-A / B is odd, and X1 + X2 is even
So this equation has no integer root

First,dig the___ .___ put the seeds___ the soil

First,dig the ( hole ) .(Then ) put the seeds (jnto ) the soil.
First, dig a hole. Then put the seed into the soil

For a rectangular grassland, its length is reduced by 5 m and its width is increased by 3 m to get a square grassland whose area is equal to that of the original rectangle
Find the area of this rectangle

Let the side length of a square be x meters
（X+5)(X-3)=X²
X²+2X-15=X²
2X=15
X=7.5
So the area of a rectangle = the area of a square = 7.5 & # 178; = 56.25 square meters

Love, talk, these, start, draw, good
Say (past tense) to (plural)

like
short
those
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paint
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said
tomatoes
Hope to help you, I use a mobile phone, can not receive follow-up, if you have any questions please send me a message, or help can also ha~

As shown in the figure, △ ABC ≌ △ ade, BC's extension line intersects DA at F, intersects de at g, ∠ ACB = ∠ AED = 105 °, ∠ CAD = 10 ° and ∠ B = ∠ d = 25 ° to calculate the degree of ∠ DFB and ∠ DGB

∵ - ACB = 105 °, ∵ B = 25 °, ∵ - BAC = 180 ° - ACB - ∵ B = 180 ° - 105 ° - 25 ° = 50 °, ∵ - CAD = 10 °, ∵ - BAF = ∵ BAC + ∵ CAD = 50 ° + 10 ° = 60 °, in △ ABF, ∵ DFB = ∵ B + ∵ BAF = 25 ° + 60 ° = 85 °; ∵ - D = 25 °, ∵ in △ DGF, ∵ DGB = ∵ DFB - ∵ d = 85 ° - 25 ° = 60 °

Past tense of play

play-played-played

Sliding rheostat partial pressure method
I can draw the circuit diagram, but I can't even draw the physical diagram. It's always strange that there are several lines in those examples

It's better to consult teachers or better students. Don't be afraid. It's very simple, but one or two words are not clear
First of all, we need to recognize the physical drawing of the equipment, especially where the terminal is. The others just need to be connected

On the quality factor of inductance capacitance parallel resonant circuit?
The definition of quality factor is not: the quality factor of resonant circuit is the ratio of characteristic impedance and circuit resistance
The loss resistance of the inductor is R. but the pure resistance of the parallel resonant circuit is r = L / (c * r), which is written in the book
But the quality factor is q = WL / R
When the inductance and capacitor parallel resonant circuit resonates, the resistance is not r = L / (c * r). Why is the resistance used to calculate the quality factor R
3q
Don't disturb the first floor!

The original definition of Q value of inductance coil is: at a given frequency, the ratio of the maximum energy stored in the coil to the total loss energy in each cycle is 2pi times. Q = WLS / R (Q of inductance series equivalent circuit); q = R / WLP (Q of inductance parallel equivalent circuit)