R S Aggarwal Solutions for Exercise 1: EXERCISE 2A

Show that: $1+i^{10}+i^{100}-i^{1000}=0$

Show that: $i^{104}+i^{109}+i^{114}+i^{119}=0$

Show that: $6i^{54}+5i^{37}-2i^{11}+6i^{68}=7i$

Show that: $\frac{1}{i}-\frac{1}{i^2}+\frac{1}{i^3}-\frac{1}{i^4}=0$

Show that: $\left(1+i^{14}+i^{18}+i^{22}\right)$ is a real number.

Evaluate: $\sqrt{-81}$

Evaluate: $\sqrt{-25}\times \sqrt{-81}$

Evaluate: $4\sqrt{-4}+5\sqrt{-9}-3\sqrt{-16}$