Basic Math Examples

$\frac{9 - 4 i^{2}}{3 + 2 i}$

Step 1

Multiply the numerator and denominator of $\frac{9 - 4 i^{2}}{3 + 2 i}$ by the conjugate of $3 + 2 i$ to make the denominator real.

$\frac{9 - 4 i^{2}}{3 + 2 i} \cdot \frac{3 - 2 i}{3 - 2 i}$

Step 2

Multiply.

Tap for more steps...

Step 2.1

Combine.

$\frac{(9 - 4 i^{2}) (3 - 2 i)}{(3 + 2 i) (3 - 2 i)}$

Step 2.2

Simplify the numerator.

Tap for more steps...

Step 2.2.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1

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

$\frac{(9 - 4 \cdot - 1) (3 - 2 i)}{(3 + 2 i) (3 - 2 i)}$

Step 2.2.1.2

Multiply $- 4$ by $- 1$ .

$\frac{(9 + 4) (3 - 2 i)}{(3 + 2 i) (3 - 2 i)}$

Step 2.2.2

Add $9$ and $4$ .

$\frac{13 (3 - 2 i)}{(3 + 2 i) (3 - 2 i)}$

Step 2.2.3

Apply the distributive property.

$\frac{13 \cdot 3 + 13 (- 2 i)}{(3 + 2 i) (3 - 2 i)}$

Step 2.2.4

Multiply $13$ by $3$ .

$\frac{39 + 13 (- 2 i)}{(3 + 2 i) (3 - 2 i)}$

Step 2.2.5

Multiply $- 2$ by $13$ .

$\frac{39 - 26 i}{(3 + 2 i) (3 - 2 i)}$

Step 2.3

Simplify the denominator.

Tap for more steps...

Step 2.3.1

Expand $(3 + 2 i) (3 - 2 i)$ using the FOIL Method.

Tap for more steps...

Step 2.3.1.1

Apply the distributive property.

$\frac{39 - 26 i}{3 (3 - 2 i) + 2 i (3 - 2 i)}$

Step 2.3.1.2

Apply the distributive property.

$\frac{39 - 26 i}{3 \cdot 3 + 3 (- 2 i) + 2 i (3 - 2 i)}$

Step 2.3.1.3

Apply the distributive property.

$\frac{39 - 26 i}{3 \cdot 3 + 3 (- 2 i) + 2 i \cdot 3 + 2 i (- 2 i)}$

Step 2.3.2

Simplify.

Tap for more steps...

Step 2.3.2.1

Multiply $3$ by $3$ .

$\frac{39 - 26 i}{9 + 3 (- 2 i) + 2 i \cdot 3 + 2 i (- 2 i)}$

Step 2.3.2.2

Multiply $- 2$ by $3$ .

$\frac{39 - 26 i}{9 - 6 i + 2 i \cdot 3 + 2 i (- 2 i)}$

Step 2.3.2.3

Multiply $3$ by $2$ .

$\frac{39 - 26 i}{9 - 6 i + 6 i + 2 i (- 2 i)}$

Step 2.3.2.4

Multiply $- 2$ by $2$ .

$\frac{39 - 26 i}{9 - 6 i + 6 i - 4 i i}$

Step 2.3.2.5

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

$\frac{39 - 26 i}{9 - 6 i + 6 i - 4 (i^{1} i)}$

Step 2.3.2.6

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

$\frac{39 - 26 i}{9 - 6 i + 6 i - 4 (i^{1} i^{1})}$

Step 2.3.2.7

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

$\frac{39 - 26 i}{9 - 6 i + 6 i - 4 i^{1 + 1}}$

Step 2.3.2.8

Add $1$ and $1$ .

$\frac{39 - 26 i}{9 - 6 i + 6 i - 4 i^{2}}$

Step 2.3.2.9

Add $- 6 i$ and $6 i$ .

$\frac{39 - 26 i}{9 + 0 - 4 i^{2}}$

Step 2.3.2.10

Add $9$ and $0$ .

$\frac{39 - 26 i}{9 - 4 i^{2}}$

Step 2.3.3

Simplify each term.

Tap for more steps...

Step 2.3.3.1

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

$\frac{39 - 26 i}{9 - 4 \cdot - 1}$

Step 2.3.3.2

Multiply $- 4$ by $- 1$ .

$\frac{39 - 26 i}{9 + 4}$

Step 2.3.4

Add $9$ and $4$ .

$\frac{39 - 26 i}{13}$

Step 3

Cancel the common factor of $39 - 26 i$ and $13$ .

Tap for more steps...

Step 3.1

Factor $13$ out of $39$ .

$\frac{13 \cdot 3 - 26 i}{13}$

Step 3.2

Factor $13$ out of $- 26 i$ .

$\frac{13 \cdot 3 + 13 (- 2 i)}{13}$

Step 3.3

Factor $13$ out of $13 (3) + 13 (- 2 i)$ .

$\frac{13 (3 - 2 i)}{13}$

Step 3.4

Cancel the common factors.

Tap for more steps...

Step 3.4.1

Factor $13$ out of $13$ .

$\frac{13 (3 - 2 i)}{13 (1)}$

Step 3.4.2

Cancel the common factor.

$\frac{13 (3 - 2 i)}{13 \cdot 1}$

Step 3.4.3

Rewrite the expression.

$\frac{3 - 2 i}{1}$

Step 3.4.4

Divide $3 - 2 i$ by $1$ .

$3 - 2 i$