Maths Book back answers and solution for Exercise questions - Mathematics : Complex Numbers: Geometry and Locus of Complex Numbers: Problem Questions with Answer, Solution

EXERCISE 2.6

1. If *z *= *x *+ *iy *is a complex number such that

show that the locus of *z *is real axis.

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

2*x**2* + 2 *y**2* + *x *- 2 *y *= 0.

3. Obtain the Cartesian form of the locus of *z *= *x *+ *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 â€“ *i*| = 3

(ii) |2z + 2 - 4*i*| = 2

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

5. Obtain the Cartesian equation for the locus of *z *= *x *+ *iy *in each of the following cases:

(i) |z â€“ 4| = 16

(ii) |z â€“ 4|2 - |z -1|2 = 16 .

Answers:

Tags : Problem Questions with Answer, Solution , 12th Mathematics : UNIT 2 : Complex Numbers

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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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