Simplify (-1+5i)/i

$\frac{- 1 + 5 i}{i}$

Step 1

Multiply the numerator and denominator of $\frac{- 1 + 5 i}{i}$ by the conjugate of $i$ to make the denominator real.

$\frac{- 1 + 5 i}{i} \cdot \frac{i}{i}$

Step 2

Multiply.

Combine.

$\frac{(- 1 + 5 i) i}{i i}$

Simplify the numerator.

Apply the distributive property.

$\frac{- 1 i + 5 i i}{i i}$

Rewrite $- 1 i$ as $- i$ .

$\frac{- i + 5 i i}{i i}$

Multiply $5 i i$ .

Raise $i$ to the power of $1$ .

$\frac{- i + 5 (i^{1} i)}{i i}$

Raise $i$ to the power of $1$ .

$\frac{- i + 5 (i^{1} i^{1})}{i i}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- i + 5 i^{1 + 1}}{i i}$

Add $1$ and $1$ .

$\frac{- i + 5 i^{2}}{i i}$

Simplify each term.

Rewrite $i^{2}$ as $- 1$ .

$\frac{- i + 5 \cdot - 1}{i i}$

Multiply $5$ by $- 1$ .

$\frac{- i - 5}{i i}$

Reorder $- i$ and $- 5$ .

$\frac{- 5 - i}{i i}$

Simplify the denominator.

Raise $i$ to the power of $1$ .

$\frac{- 5 - i}{i^{1} i}$

Raise $i$ to the power of $1$ .

$\frac{- 5 - i}{i^{1} i^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- 5 - i}{i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{- 5 - i}{i^{2}}$

Rewrite $i^{2}$ as $- 1$ .

$\frac{- 5 - i}{- 1}$

Step 3

Simplify the expression.

Move the negative one from the denominator of $\frac{- 5 - i}{- 1}$ .

$- 1 \cdot (- 5 - i)$

Rewrite $- 1 \cdot (- 5 - i)$ as $- (- 5 - i)$ .

$- (- 5 - i)$

Step 4

Apply the distributive property.

$- - 5 - - i$

Step 5

Multiply.

Multiply $- 1$ by $- 5$ .

$5 - - i$

Multiply $- 1$ by $- 1$ .

$5 + 1 i$

Multiply $i$ by $1$ .

$5 + i$

Simplify (-1+5i)/i

Related Questions

Support LCMGCF.com by disabling your adblocker.