Question

The value of $\frac{i^{592}+i^{590}+i^{588}+i^{586}+i^{584}}{i^{582}+i^{580}+i^{578}+i^{576}+i^{574}}$ -1 is

• A. -1
• B. -2
• C. -3
• D. -4

Answer 1

The correct option is B

-2

$\frac{i^{592}+i^{590}+i^{588}+i^{586}+i^{584}}{i^{582}+i^{580}+i^{578}+i^{576}+i^{574}}-1=\frac{i^{4\times 148}+i^{4\times 147+2}+i^{4\times 147}+i^{4\times 146+2}+i^{4\times 146}}{i^{4\times 145+2}+i^{4\times 145}+i^{4\times 144+2}{i}^{4\times 144}+i^{4\times 143+2}}-1[\because i^4=1\text{and}{i}^2=-1]=\frac{1+i^2+1+i^2+1}{i^2+1+i^2+1+i^2}-1=\frac{1}{-1}-1=-2$