What is (2i^8+2i^{-7})/(i^{11)+1} ?

The solution to (2i^8+2i^{-7})/(i^{11)+1} is 2i

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simplify (2i^8+2i^{-7})/(i^{11)+1}

simplify

\frac{2 i ^{8} + 2 i ^{- 7}}{i ^{11} + 1}

2 i

Solution steps

\frac{2 i ^{8} + 2 i ^{- 7}}{i ^{11} + 1}

2 i^{8} = 2

i^{- 7} = i

= \frac{2 + 2 i}{i ^{11} + 1}

Factor

2 + 2 i : 2 (1 + i)

= \frac{2 ( 1 + i )}{i ^{11} + 1}

Factor

i^{11} + 1 : - (i + 1) i

= \frac{2 ( 1 + i )}{- ( i + 1 ) i}

Apply the commutative law:

1 + i = i + 1

= \frac{2 ( i + 1 )}{- ( i + 1 ) i}

Cancel the common factor:

i + 1

= \frac{2}{- i}

Simplify

\frac{2}{- i} : 2 i

= 2 i

8 a + 2 (1 - 5 a) \leq 20

7 (x - 2) = 5 (x + 2)

10 p^{2} + 4 p + 77 = 9

x = (3 \cdot 9 \cdot (3 + (\frac{9 \cdot 3}{3})))

16 x^{2} + 9 = 5

What is (2i^8+2i^{-7})/(i^{11)+1} ?
The solution to (2i^8+2i^{-7})/(i^{11)+1} is 2i