Simplify (7-3i)*(2-i)

$(7 - 3 i) \cdot (2 - i)$

Step 1

Expand $(7 - 3 i) (2 - i)$ using the FOIL Method.

Apply the distributive property.

$7 (2 - i) - 3 i (2 - i)$

Apply the distributive property.

$7 \cdot 2 + 7 (- i) - 3 i (2 - i)$

Apply the distributive property.

$7 \cdot 2 + 7 (- i) - 3 i \cdot 2 - 3 i (- i)$

$7 \cdot 2 + 7 (- i) - 3 i \cdot 2 - 3 i (- i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $7$ by $2$ .

$14 + 7 (- i) - 3 i \cdot 2 - 3 i (- i)$

Multiply $- 1$ by $7$ .

$14 - 7 i - 3 i \cdot 2 - 3 i (- i)$

Multiply $2$ by $- 3$ .

$14 - 7 i - 6 i - 3 i (- i)$

Multiply $- 3 i (- i)$ .

Multiply $- 1$ by $- 3$ .

$14 - 7 i - 6 i + 3 i i$

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

$14 - 7 i - 6 i + 3 (i^{1} i)$

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

$14 - 7 i - 6 i + 3 (i^{1} i^{1})$

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

$14 - 7 i - 6 i + 3 i^{1 + 1}$

Add $1$ and $1$ .

$14 - 7 i - 6 i + 3 i^{2}$

$14 - 7 i - 6 i + 3 i^{2}$

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

$14 - 7 i - 6 i + 3 \cdot - 1$

Multiply $3$ by $- 1$ .

$14 - 7 i - 6 i - 3$

$14 - 7 i - 6 i - 3$

Subtract $3$ from $14$ .

$11 - 7 i - 6 i$

Subtract $6 i$ from $- 7 i$ .

$11 - 13 i$

$11 - 13 i$

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