Question:
Prove that $6 i^{50}+5 i^{33}-2 i^{15}+6 i^{48}=7 i$
Solution:
Given: $6 i^{50}+5 i^{33}-2 i^{15}+6 i^{48}$
To prove: $6 i^{50}+5 i^{33}-2 i^{15}+6 i^{48}=7 i$
$\Rightarrow 6 i^{4 \times 12+2}+5 i^{4 \times 8+1}-2 i^{4 \times 3+3}+6 i^{4 \times 12}$
$\Rightarrow 6 i^{2}+5 i^{1}-2 i^{3}+6 i^{0}$
$\Rightarrow-6+5 i+2 i+6$
$\Rightarrow 7 \mathrm{i}$
$\Rightarrow$ L.H.S $=$ R.H.S
Hence proved.