Simplify (1+i)(3-2i)

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

Step 1

Expand $(1 + i) (3 - 2 i)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $1$ .

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

Multiply $- 2 i$ by $1$ .

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

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

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

Multiply $i (- 2 i)$ .

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

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

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

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

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

$3 - 2 i + 3 i - 2 i^{1 + 1}$

Add $1$ and $1$ .

$3 - 2 i + 3 i - 2 i^{2}$

$3 - 2 i + 3 i - 2 i^{2}$

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

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

Multiply $- 2$ by $- 1$ .

$3 - 2 i + 3 i + 2$

$3 - 2 i + 3 i + 2$

Add $3$ and $2$ .

$5 - 2 i + 3 i$

Add $- 2 i$ and $3 i$ .

$5 + i$

$5 + i$

Related Questions