Simplify (1+i)*(3-5i)

$(1 + i) \cdot (3 - 5 i)$

Step 1

Expand $(1 + i) (3 - 5 i)$ using the FOIL Method.

Apply the distributive property.

$1 (3 - 5 i) + i (3 - 5 i)$

Apply the distributive property.

$1 \cdot 3 + 1 (- 5 i) + i (3 - 5 i)$

Apply the distributive property.

$1 \cdot 3 + 1 (- 5 i) + i \cdot 3 + i (- 5 i)$

$1 \cdot 3 + 1 (- 5 i) + i \cdot 3 + i (- 5 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $1$ .

$3 + 1 (- 5 i) + i \cdot 3 + i (- 5 i)$

Multiply $- 5 i$ by $1$ .

$3 - 5 i + i \cdot 3 + i (- 5 i)$

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

$3 - 5 i + 3 \cdot i + i (- 5 i)$

Multiply $i (- 5 i)$ .

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

$3 - 5 i + 3 i - 5 (i^{1} i)$

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

$3 - 5 i + 3 i - 5 (i^{1} i^{1})$

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

$3 - 5 i + 3 i - 5 i^{1 + 1}$

Add $1$ and $1$ .

$3 - 5 i + 3 i - 5 i^{2}$

$3 - 5 i + 3 i - 5 i^{2}$

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

$3 - 5 i + 3 i - 5 \cdot - 1$

Multiply $- 5$ by $- 1$ .

$3 - 5 i + 3 i + 5$

$3 - 5 i + 3 i + 5$

Add $3$ and $5$ .

$8 - 5 i + 3 i$

Add $- 5 i$ and $3 i$ .

$8 - 2 i$

$8 - 2 i$

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