Solution of complex equation How to solve Z ^ 4 = 2Z? Let's know whether to use university knowledge or high school knowledge

Solution of complex equation How to solve Z ^ 4 = 2Z? Let's know whether to use university knowledge or high school knowledge

Firstly, the equation is reduced to Z (Z ^ 3-2) = 0, and the solution is Z = 0 or Z ^ 3 = 2
So in the range of real number, we can get z = 0 or Z = 3 root sign 2
In the range of complex number, there are two solutions
High school method: 2 = 2 (COS 360 ° + isin 360 °) (where I is an imaginary unit)
If we divide 360 ° into three equal parts, we can get 0 °, 120 ° and 240 °, so Z ^ 3 = 2 has three
Z1 = root 2 of degree 3 (cos0 ° + isin0 °)
Z2 = root 2 of degree 3 (cos120 ° + isin120 °)
Z1 = root 2 of degree 3 (COS 240 ° + isin 240 °)
Where Z1 is the real solution
University solution: Z ^ 3 = 2, z = e ^ (IK π / 3) is obtained from Euler formula, where k = 0,1,2
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We know the equation x ^ 2 + 2x + M = 0 (m ∈ R) about X
If α and β are two imaginary roots of the equation and | α | + | β | = 4, find the value of M and the solution set of the equation

X & sup2; + 2x + M = 0 (x + 1) & sup2; = (1-m) = (m-1) I & sup2; (where I & sup2; = - 1) x + 1 = ± (√ (m-1)) IX = ± (√ (m-1)) I - 1 because | α | + | β | = 4, | 2 √ [(√ (m-1)) & sup2; + 1 & sup2;] = 4 (m-1) + 1 = 4m = 4 the solution of the equation is: - 1 ± √ 3

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B C English_ Country_ Broadcasting Company U N UN WC toilet KFC KFC W T O World Trade Organization VOA USA_ Country_ Voice of America ABC CCTV_ Country_ Medium_ Central_ TV station U K UK CD R M B_ People_ PE Sports IQ EQ EQ ok

What of it?

I can wear a red tie with a pink shire if I want to.What You're not having your mean just now, I hope

A fraction is reduced to & nbsp; 45. If the numerator of the fraction is reduced by 124 and the denominator by 11, the new fraction is reduced to 49. What is the original fraction?

Let the original score be 4x5x. From the question meaning 4x − 1245x − 11 = 49, the solution is x = 67, so the original score is 4 × 675 × 67 = 268335

Each a pair of shoes?
I don't know if it's right. If it's right, do you use the singular or the plural?
thank you

Because of each pair of shoes, the singular number is used

If the square of X - the square of y = 48, x + y = 6, then 3x - 3Y =?
Process I don't know! Please write the process! Thank you!

Square of X - square of y = 48
(x + y) (X-Y) = 48 (square difference formula)
Because x + y = 6
So X-Y = 48 / 6 = 8
3x-3y=3(x-y)=3x8=24

English translation
1、 do something heart and ______
2、full of ______ fervor

1. Soul heart and soul
2. Patent / relative and so on

The edge BC of triangle ABC is 48CM, the height ad is 16cm, the edge FG of rectangle efgh is on BC, the vertex E and H are on AB and AC respectively, the ratio of EF and FG of adjacent sides is 5:9
The edge BC of triangle ABC is 48CM, the height ad is 16cm, the edge FG of rectangle efgh is on BC, the vertex E and H are on AB and AC respectively, the ratio of EF and FG of adjacent sides is 5:9, the perimeter of rectangle efgh is calculated

Let EF = 5x, FG = 9x, then (16-5x) * 9x / 2 + 5x * (48-9x) / 2 + 5x * 9x = 48 * 16 / 2, the solution is x = 2, then EF = 5 * 2 = 10, FG = 9 * 2 = 18, then the perimeter of rectangular efgh = (10 + 18) * 2 = 56cm

Who knows if every boy and girl and every boy and every girl are followed by be in singular or plural
eg:Every boy and girl in Britain has read it
Every boy and every girl in Britain

Every boy and every girl has the right to receive education