Let Z satisfy | z-1-2i | = 1, (1) find the maximum value of | Z | (2) find the maximum value of | Z - (2 + I) |

Let Z satisfy | z-1-2i | = 1, (1) find the maximum value of | Z | (2) find the maximum value of | Z - (2 + I) |

|Z-1-2i|>=|Z|-|1+2i|
|Z-1-2i|>=|1+2i|-|Z|
sqrt(5)-1
Solution: consider the equation of circle
(1) | z-1-2i | = 1 denotes the point on the circle with 1 + 2I as the center and 1 as the radius on the complex plane
So | 1 + 2I | - 1 ≤ | Z ≤ | 1 + 2I | + 1
That is: - 1 + √ 5 ≤ | Z | ≤ 1 + √ 5
(2) | Z - (2 + I) | is the distance from the point on the above circle to (2 + I)
|1 + 2I - (2 + I) | - 1 ≤| Z - (2 + I) | ≤| 1 + 2I - (2 + I) | +... Expansion
Solution: consider the equation of circle
(1) | z-1-2i | = 1 denotes the point on the circle with 1 + 2I as the center and 1 as the radius on the complex plane
So | 1 + 2I | - 1 ≤ | Z ≤ | 1 + 2I | + 1
That is: - 1 + √ 5 ≤ | Z | ≤ 1 + √ 5
(2) | Z - (2 + I) | is the distance from the point on the above circle to (2 + I)
|1+2i-(2+i)| -1 ≤|z-(2+i)| ≤|1+2i-(2+i)| +1
That is: - 1 + √ 2 ≤ | Z - (2 + I) | ≤ 1 + √ 2
The title of complex number: given | Z | = 1, find the maximum value of | Z - (2 + 2I) |
Graphic method,
The problem is equivalent to the maximum distance from (2,2) on the unit circle
Draw a picture to see that the maximum value is 2 times the root, then add 1
The minimum value is 2 times the root of 2 and then 1
2√2-1
Why is m 2 + M 2 + m 2-m 2 + m 2-m 2
(1) Z is a pure imaginary number (2), and the corresponding point is on the straight line x + y + 3 = 0
Z=(m2+m-2)+(m2+2m-3)i
=(m-1)(m+2)+(m-1)(m+3)i
(1) Z is a pure imaginary number
So (m-1) (M + 2) = 0
(m-1) (M + 3) is not equal to 0
So m = - 2
(2) The corresponding point is on the line x + y + 3 = 0
m-1)(m+2)+(m-1)(m+3)+3=0
m=0.5 -2
Is the plural or singular of the noun after the other~
Is it singular or plural or both?
The other can be followed by a singular or plural noun
After the other, the singular means "the other one." when the plural means "the other part."
singular
complex
singular
Given the complex number Z = 1-I (I is an imaginary unit), if a ∈ r such that AZ + 2Z ∈ R, then a=______ .
Because of the complex z = 1-I, AZ + 2Z = A1 − I + 2-2i = a (1 + I) (1 − I) (1 + I) + 2-2i = A2 + 2-2i + a2i, because AZ + 2Z ∈ R, so 2-A2 = 0, a = 4
The plural of nouns as adjectives
21．—What kind of dumplings would you like?
—I’d like some dumplings．
A．cabbage B．carrots C．onions D．eggs
When nouns are used as attributives to modify nouns, singular numbers should be used, such as cage dumpings, with a few exceptions, such as women teachers
A
Just like apple tree
A
Is any other followed by a noun singular or plural?
He is taller than any other student in our class
Plural question. 0.0
Calculation (1-2i) + (- 2 + 3I) + (3-4i) + (- 4 + 5I) +. + (- 2006 + 2007I) + (2007-2008i)
The original formula = [- 2) + (3) + (3) + (2) + (2) + (3) + (3) + (2) + (3) + (3) + (3) + (2) + (3) + (2) + (3) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + (2) + ( +（2005-2006）+2007]+[(-2+3)+(-4+5)+… +（-2006+2007）-2008]i
=[-2006/2+2007]+[2006/2-2008]i
=1004-1005i
Original formula = (- 1) × 1003 + 2007 + 1003i-2008i = 1004-1005i
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Singular and plural forms of nouns and adjectives_
Please talk about the master, under what circumstances how deformation + s what
Of course, it depends on the context, except for some special cases with the same singular and plural
Can you add countable nouns after kind of, singular, plural, and uncountable nouns?
Kind of modifies adjectives and adverbs to express "a little bit", such as "kind of Henry"
A kind of modifies a noun to indicate a kind, such as a kind of book
What does it mean to add a countable noun singular