EXERCISE 2.5

EXERCISE 2.5 1. Find the modulus of the following complex numbers (i) (ii) 2 1 2 (iii) ( − i (iv) 2 3 )( 2. For any two complex numbers z 1 and z 2 , such that z = and z z 1 2 , then show that z z 1 2 is a real number. 3. Which one of the points 10 − i , 11 + i is closest to1 + i . 4. If | | z = 3, show that 7 13 + − 5. If z = 1, show that 2 6. If | | z = 2, show that 8 + + 7. If z , and z 3 are three complex numbers such that z , show that 9 1 2 1 3 z z z z z z 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 has five solutions. 10. Find the square roots of (i) 4 + i (ii) 8 i (iii) −− 5 12 i . 12th_Maths_EM_Vol1_CH 2_Complex Numbers.indd 72 16-12-2022 12:27:52 Complex Numbers