Basic Math Examples

$15 + 10 i^{5} \div (- 3) - i$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite the division as a fraction.

$15 + \frac{10 i^{5}}{- 3} - i$

Step 1.2

Simplify the numerator.

Tap for more steps...

Step 1.2.1

Factor out $i^{4}$ .

$15 + \frac{10 (i^{4} i)}{- 3} - i$

Step 1.2.2

Rewrite $i^{4}$ as $1$ .

Tap for more steps...

Step 1.2.2.1

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$15 + \frac{10 ({(i^{2})}^{2} i)}{- 3} - i$

Step 1.2.2.2

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

$15 + \frac{10 ({(- 1)}^{2} i)}{- 3} - i$

Step 1.2.2.3

Raise $- 1$ to the power of $2$ .

$15 + \frac{10 (1 i)}{- 3} - i$

Step 1.2.3

Multiply $i$ by $1$ .

$15 + \frac{10 i}{- 3} - i$

Step 1.3

Move the negative in front of the fraction.

$15 - \frac{10 i}{3} - i$

Step 2

To write $- i$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$15 - \frac{10 i}{3} - i \cdot \frac{3}{3}$

Step 3

Combine $- i$ and $\frac{3}{3}$ .

$15 - \frac{10 i}{3} + \frac{- i \cdot 3}{3}$

Step 4

Simplify the expression.

Tap for more steps...

Step 4.1

Combine the numerators over the common denominator.

$15 + \frac{- 13 i}{3}$

Step 4.2

Move the negative in front of the fraction.

$15 - \frac{13 i}{3}$