# Complex numbers

**Exercise 13.1**

QUESTION 1

Evaluate the following:

(i)

Sol :

(ii)

Sol :

=1

(iii)

Sol :

= -1

(iv)

Sol :

(v)

Sol :

= 0

(vi)

Sol :

= 0

(vii)

Sol :

= 1

(viii)

Sol :

QUESTION 2

Show that

Sol :

= 0 which is a real number

Hence, proved

QUESTION 3

Find the values for the following expressions:

(i)

Sol :

(ii)

Sol :

[\because i^2=-1]

= 1

(iii)

Sol :

= 0

(iv)

Sol :

[\because~(i^2=-1)~(i^3=-i)]

= -1

(v)

Sol :

= -1

(vi)

Sol :

.

.

.

[As, there are 11 terms]

= 1

(vii)

Sol :