Unit – 1

Complex Numbers

Question and answer

1. Express in the form of a + ib :

2.     find the modulus of

3.     If then show that are   conjugate complex numbers?

       Let

Also

Again

Hence both of them are conjugate to each other.

4.     Find the value of

Sol:

5.     Find the value of

Sol:  

6.     If are the roots of the equation .prove that

Sol: If are the roots of the equation

       Therefore

             So,

                                  }

                                    =

7.     Prove that

                                    -

8.     Expand the in power of sine

9.     Prove that

Sol: Using 

10. If  z is fifth root of unity i.e. then find all the values of z?

Sol: Given

Therefore roots of z are 1,

Try: find the square root of

11. form the equation whose roots are

      Let

            Therefore

                   When ( y - 1 )=0  this gives

                        by re arranging

           Dividing each term by

             Therefore

                           …….     (i)

             Since

              Also  

                  Hence roots of the equation (i) are