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Problem Questions with Answer, Solution - Exercise 2.6: Geometry and Locus of Complex Numbers | 12th Mathematics : UNIT 2 : Complex Numbers

Chapter: 12th Mathematics : UNIT 2 : Complex Numbers

Exercise 2.6: Geometry and Locus of Complex Numbers

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EXERCISE 2.6

1. If iy is a complex number such that 

show that the locus of is real axis.



2. If iy is a complex number such that Im  = 0 , show that the locus of is

2x2 + 2 y2 + - 2 = 0.



3. Obtain the Cartesian form of the locus of iy in each of the following cases:

(i)  [Re (iz )]2 = 3  

(ii) Im[(1- i)z +1] = 0

(iii) |z + i| = |z -1|

(iv)  = z-1.



4. Show that the following equations represent a circle, and, find its centre and radius.

(i) |z - 2 – i| = 3

(ii) |2z + 2 - 4i| = 2 

(iii) |3z - 6 +12i| = 8



5. Obtain the Cartesian equation for the locus of iy in each of the following cases:

(i)  |z – 4| = 16

(ii) |z – 4|2 - |z -1|2 = 16 .



Answers:


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12th Mathematics : UNIT 2 : Complex Numbers : Exercise 2.6: Geometry and Locus of Complex Numbers | Problem Questions with Answer, Solution

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12th Mathematics : UNIT 2 : Complex Numbers


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