The real part and imaginary part conjugate complex angles and their principal values of Z = 1 / I + 3I / 1-I

The real part and imaginary part conjugate complex angles and their principal values of Z = 1 / I + 3I / 1-I

Reduced z = - 3 / 2 + I / 2
So the real part is - 3 / 2 and the imaginary part is 1 / 2
The conjugate complex number is Z1 = - 3 / 2-I / 2
The depression angle is k π + arctan (- 1 / 3)
The principal value is arctan (- 1 / 3)
It is known that z is an imaginary number. The sufficient and necessary condition for proving that Z + 1 / Z is a real number is | Z | = 1
Z + 1 / Z is a real number
z+1/z=z'+1/z'
zzz'+z'=zz'z'+z
(z-z')(zz'-1)=0
And Z is an imaginary number, Z ≠ Z ', so (Z-Z') (ZZ '- 1) = 0zz' = 1 | Z | = 1
Where Z 'is the conjugate of Z
(1) Given that z is an imaginary number, the necessary and sufficient condition to prove that Z + 1 / Z is a real number is | Z | = 1
(2) To prove that | is a pure complex number ≠ Z-1
[Note: (1) because it is difficult to type, we can remember that the conjugate complex of complex Z is Z '. (2) several conclusions: (!). | Z | ^ 2 = | Z' | ^ 2 = Z * Z '. (!). The sufficient and necessary condition for Z to be a real number is Z = Z'. (!) the sufficient and necessary condition for Z to be a pure imaginary number is Z + Z '= 0. (!) the sufficient and necessary condition for ZZ to be an imaginary number is Z-Z' ≠ 0
You can ask the teacher. It's easy to understand
Let the complex number Z satisfy: 3z-5 = I (Z + 5), (I is an imaginary unit) to find the minimum value of (1) | Z | (2) | z-a-ai | (a belongs to R)
As a result, 3m-5 = -n, M + 5 = 3 n. the solution is: M = 1, n = 2.z = 1 + 2.z = 1 + 2I (1) I (3 (3 + Ni) - 3 (M + Ni) - 5 = I (M + 5) (3m + 5) (3m-5) (3m-5) (3m-5) (3m-5) (3m-5) (3m-5) (3m-5) (3m-5) + (3Ni (M + 5) so, 3m-5 = -5-n, 3m-5 = -n-n, m-5 = N-N-N, m-5 = 1, n = 2. The solution: M = 1, n = 1, n = 2, n = 2.z = 2 (2) (2 (2) z-z-z-a-z-a-a-a-a-a-a-a) i-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a a -
Let z = a + bi, then: 3 (a + bi) - 5 = I (a + 5 + bi)
So: 3a-5 = - B, 3b = a + 5
So: a = 1, B = 2
|z|=√(1²+2²)=√5
|z-a-ai|=√[(1-a)²+(2-a)²]=√[2(a-1.5)²+0.5]≥√0.5
1. Root 5 2, 2 / 2 root 2
Let the complex number Z satisfy: 3z-5 = I (Z + 5), (I is an imaginary unit) to find the minimum value of (1) | Z | (2) | z-a-ai | (a belongs to R)
Let z = x + Yi; then 3 (x + Yi) - 5 = I (x + Yi + 5); that is, 3x-5 + 3yi = - y + (x + 5) I; that is, 3x + Y-5 + (- x + 3y-5) I = 0
So there are 3x + Y-5 = 0...... (1); - x + 3y-5 = 0...... (2)
From (2), we obtain x = 3y-5,... Expansion
Let the complex number Z satisfy: 3z-5 = I (Z + 5), (I is an imaginary unit) to find the minimum value of (1) | Z | (2) | z-a-ai | (a belongs to R)
Let z = x + Yi; then 3 (x + Yi) - 5 = I (x + Yi + 5); that is, 3x-5 + 3yi = - y + (x + 5) I; that is, 3x + Y-5 + (- x + 3y-5) I = 0
So there are 3x + Y-5 = 0...... (1); - x + 3y-5 = 0...... (2)
From (2), we get x = 3y-5, and substitute (1) to get 3 (3y-5) + Y-5 = 10y-20 = 0, so y = 2, x = 6-5 = 1;
∴z=1+2i
(1)︱z︱=√(1+2²)=√5
(2).︱z-a-ai︱=︱(1-a)+(2-a)i︱=√[(1-a)²+(2-a)²]=√[2(a²-3a)+5]
=√[2(a-3/2)²-9/2+5]=√[2(a-3/2)²+1/2]≧(√2)/2
The minimum value of z-a-ai is (√ 2) / 2. Put it away
The pronunciation of verb noun of the same word
Some words can be used as nouns and verbs, pronunciation of stress syllables, one in the front, one in the back. But some words pronunciation rules are not like this, what rules?
But some pronunciation rules are not like this, such as advocate, verb and noun stress all in front, why
When you use a verb, you should put the stress at the back; when you use a noun, you should put the stress at the front
for example
record
n. ['rek &;: D] record, video v. [ri'k &; D] record. At the same time, re also needs to change its voice
Later, we will find the rules gradually. I hope you can come on and learn better!
If the complex Z satisfies the equation Z ^ 2 + 2 = 0, then Z ^ 3=
If z = - 2I is calculated here, I will not. Is it equal to - 8i ^ 3
But the answer is 2I under plus or minus 2
z^2=-2
Z = 2I under root
Z ^ 3 = - 2I under root 2
I'm sorry I can't make a radical
I was wrong.
It should be z = 2I under the positive and negative root sign
We need to improve. Please forgive me
Use the root formula of quadratic equation of one variable to find out Z, and then find out the next step. Tell you the best way
this is_ A map__ This is my flower
this is_ A map__ What is this / what's this
This is my flowers: These are my / our flowers
1 What's this in English ?
2 These are my flowers .
What is this in English?
These are my/our flowers
What is it in English ？
These are my flowers.
What's this in English?
1.This is_ A map__ In English
What is this in English?
2. This is my flower
These are our flowers.
Write the singular, present and the third participle of the past
1.become
2.begin
3.give
4.think
5.teach
6.catch
7.take
8.know
9.tell
10.fall
11.fly
12.cost
13.keep
14.hurt
15.write
16.stop
17.study
18.chat
1.become becomes becoming became2.begin begins beginning began3.give gives giving gave 4.think thinks thinking thought5.teach teaches teaching taught 6.catch catches catching caught7.take takes taking...
The solution of the equation Z ^ 2-2 | Z | + 1 = 0 in the complex set is___ For detailed process
If Z is a real number, then (| Z | - 1) ^ 2 = 0 is known, so | Z | = 1, and the solution is Z = - 1 or 1;
If Z is an imaginary number, let z = x + Yi (Y ≠ 0),
The equation is x ^ 2-y ^ 2 + 2xyi-2 √ (x ^ 2 + y ^ 2) + 1 = 0,
So x ^ 2-y ^ 2-2 √ (x ^ 2 + y ^ 2) + 1 = 0, and 2XY = 0,
The solution is x = 0, y = ± 1 ± √ 2,
So there are six solutions: z = - 1; 1; (- 1 - √ 2) I; (- 1 + √ 2) I; (1 - √ 2) I; (1 + √ 2) I
Is this an English book
Are these English books
Are these English books?
Are these English books？
I don't understand. Are those an English books?
this an english book