Problem Questions with Answer, Solution - Exercise 2.5: Modulus of a Complex Number | 12th Mathematics : UNIT 2 : Complex Numbers
Chapter: 12th Mathematics : UNIT 2 : Complex Numbers
Exercise 2.5: Modulus of a Complex Number
EXERCISE 2.5
1. Find the modulus of the following complex numbers
2. For any two complex numbers z1 and z2 , such that |z1| = |z2| = 1 and z1z2 ≠-1, then show that [z1 + z2] / [1+ z1z2] is a real number.
3. Which one of the points10 - 8i, 11 + 6i is closest to1+ i .
4. If | z |= 3 , show that 7 ≤ | z + 6 −8i | ≤13 .
5. If |z| = 1, show that 2 ≤ |z2 – 3| ≤ 4.
6. If 
= 2 , show that the greatest and least value of | z | are √3 +1 and √3 - 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 z3 + 2
= 0 has five solutions.
10. Find the square roots of (i) 4 + 3i (ii) -6 + 8i (iii) -5 -12i .
Answers:
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