Algebra Examples

$i (3 - 2 i) + (1 + 4 i)$

Step 1

Remove parentheses.

$i (3 - 2 i) + 1 + 4 i$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$i \cdot 3 + i (- 2 i) + 1 + 4 i$

Step 2.2

Move $3$ to the left of $i$ .

$3 \cdot i + i (- 2 i) + 1 + 4 i$

Step 2.3

Multiply $i (- 2 i)$ .

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Step 2.3.1

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

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

Step 2.3.2

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

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

Step 2.3.3

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

$3 \cdot i - 2 i^{1 + 1} + 1 + 4 i$

Step 2.3.4

Add $1$ and $1$ .

$3 \cdot i - 2 i^{2} + 1 + 4 i$

$3 \cdot i - 2 i^{2} + 1 + 4 i$

Step 2.4

Simplify each term.

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Step 2.4.1

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

$3 i - 2 \cdot - 1 + 1 + 4 i$

Step 2.4.2

Multiply $- 2$ by $- 1$ .

$3 i + 2 + 1 + 4 i$

$3 i + 2 + 1 + 4 i$

$3 i + 2 + 1 + 4 i$

Step 3

Simplify by adding terms.

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Step 3.1

Add $3 i$ and $4 i$ .

$2 + 1 + 7 i$

Step 3.2

Add $2$ and $1$ .

$3 + 7 i$

$3 + 7 i$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$