What is (i^4-i^2)/(i^3) ?

The solution to (i^4-i^2)/(i^3) is 2i

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simplify (i^4-i^2)/(i^3)

simplify

\frac{i ^{4} - i ^{2}}{i ^{3}}

2 i

Solution steps

\frac{i ^{4} - i ^{2}}{i ^{3}}

Factor

i^{4} - i^{2} : i^{2} (i^{2} - 1)

= \frac{i ^{2} ( i ^{2} - 1 )}{i ^{3}}

Factor

i^{2} - 1 : (i + 1) (i - 1)

= \frac{i ^{2} ( i + 1 ) ( i - 1 )}{i ^{3}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

i^{3} = i^{2} i

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

Cancel the common factor:

i^{2}

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

Simplify

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

= i 2

Rewrite in standard complex form:

2 i

= 2 i

- 2 + \frac{2}{5} b - \frac{1}{4} b + 6

\frac{5}{4} (- 8)

\frac{1}{3} \leq \frac{x + 1}{5} < \frac{5}{4}

6 (4 x - 10) = 84

3 x^{2} + 4 x = 1