Question

If $2i$ then $- 2i$

• A. $- 2$
• B. $2$
• C. $\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}} - 1 =$
• D. (2, 1)

Answer 1

Answer: (A)

$- 2$

Answer 2

$( 1 - i ) x + ( 1 + i ) y = 1 - 3 i$ $i^{n} + i^{n + 1} + i^{n + 2} + i^{n + 3} = i^{n}\lbrack 1 + i + i^{2} + i^{3}\rbrack$ $= i^{n}\lbrack 1 + i - 1 - i\rbrack = 0$

Equating real and imaginary parts, we get $\because(1 + i)^{2} = 1 + i^{2} + 2i = 2i$and $(1 - i)^{2} = 1 + i^{2} - 2i = - 2i$; $\Rightarrow (1 + i)^{8} + (1 - i)^{8} = (2i)^{4} + ( - 2i)^{4}$ $= 2^{4}(i^{4} + i^{4})$. Thus point is $= 2^{5} = 32.$.