5 10 15 greatest common factor least common multiple

5 10 15 greatest common factor least common multiple

5 10 15 the greatest common factor is 5
5 10 15 least common multiple 30
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If the complex Z satisfies Z-1 = 1, what is the range of Z + 2-I?
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Z-1 = 1 means that z is on the circle with (1,0) as the center and 1 as the radius
Z + 2-I = | Z - (- 2 + I) | denotes the distance from a point on a circle to (- 2,1),
Its maximum value = √ [(1 + 2) ^ 2 + 1] + 1 = 1 + √ 10
Minimum = √ [(1 + 2) ^ 2 + 1] - 1 = √ 10 - 1
So the range is [1 + √ 10, √ 10 - 1]
Radical 10-1 ＜ Z + 2-I ＜ radical 10-1
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If a ^ 2 + B ^ 2 = 4, z = a + (B + 2) I, find the value range of | Z |
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Given that z is a complex number, the modulus of Z minus 2 minus 2I is equal to one, and I is an imaginary unit, what is the minimum value of the modulus of Z plus 2 minus 2I
|If z-2-2i | = 1, Z can be regarded as the radius of a circle. If the center of the circle is (2,2), then | Z + 2-2i | can be regarded as the distance from the point (- 2,2) to the circle. The ordinate of the point and the center of the circle is exactly the same. Therefore, the minimum value of | Z + 2-2i | is the distance 4 between the point and the center of the circle minus the radius 1 = 3
Let z = a + bi, then
Z－2－2i＝a－2＋(b－2)i
(a－2)²＋(b－2)²＝1
Then 0 ≤| A-2 | ≤ 1, 0 ≤| B-2 | ≤ 1
∴1≤a≤3
Z＋2－2i＝a＋2＋(b－2)i
(a＋2)²＋(b－2)²＝(a－2)²＋(b－2)²＋4a＝1＋4a
5≤1＋4a≤13
The minimum value of the modulus of Z plus 2 minus 2I is √ 5
It can be seen from | Z - (2 + 2I) | = 1 that on the complex plane, the set of points corresponding to complex Z is a circle with radius 1 and point P (2,2) as the center. The meaning of | Z + 2-2i | = | Z - (- 2 + 2I) | is the distance from the point on the circle to Q (- 2,2). It is easy to know that | PQ | = 4. The combination of number and shape shows that | Z + 2-2i | min = 4-1 = 3
Twice as much as two minus one
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If the complex Z satisfies Z minus Z at the same time, the conjugate complex of Z is equal to 2I, and the conjugate complex of Z is equal to iz
z=a+bi
Conjugate of Z = a-bi
The conjugate complex of Z minus Z is equal to 2I
(a+bi)-(a-bi)=2bi=2i b=1
z=a+i
Conjugate of Z = A-I = (a + I) * I = - 1 + AI
a=-1
z=-1+i
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