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

EXERCISE 2.5

1. Find the modulus of the following complex numbers

2. For any two complex numbers *z*1 and *z*2 , such that |z1| = |z2| = 1 and z1z2 â‰ -1, then show that [z1 + z2] / [1+ z1z2] is a real number.

3. Which one of the points10 - 8*i*, 11 + 6*i *is closest to1+ *i *.

4. If | *z *|= 3 , show that 7 â‰¤ | *z *+ 6 âˆ’8*i *| â‰¤13 .

5. If |z| = 1, show that 2 â‰¤ |z2 â€“ 3| â‰¤ 4.

6. If = 2 , show that the greatest and least value of | z | are âˆš3 +1 and âˆš3 - 1 respectively.

7. If z1, z2, and z3 are three complex numbers such that |z1| = 1, |z2| = 2, |z3| = 3 and |z1 + z2 + z3| = 1 , show that |9z1z2 + 4z1z3 + z2z3| = 6.

8. If the area of the triangle formed by the vertices *z*, *iz *, and *z *+ *iz *is 50 square units, find the value of |z|.

9. Show that the equation *z**3* + 2* *= 0 has five solutions.

10. Find the square roots of (i) 4 + 3*i *(ii) -6 + 8*i *(iii) -5 -12*i *.

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12th Mathematics : UNIT 2 : Complex Numbers : Exercise 2.5: Modulus of a Complex Number | Problem Questions with Answer, Solution

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