How do you simplify $(6 + 3i)(-1 + 5i)$ ?

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Answer 1 · 2017-07-09T12:14:02

See a solution process below:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$(color(red)(6) + color(red)(3i))(color(blue)(-1) + color(blue)(5i))$ becomes:

$-(color(red)(6) xx color(blue)(1)) + (color(red)(6) xx color(blue)(5i)) - (color(red)(3i) xx color(blue)(1)) + (color(red)(3i) xx color(blue)(5i))$

$-6 + 30i - 3i + 15i^2$

We can now combine like terms and put in standard form:

$-6 + (30 - 3)i + 15i^2$

$-6 + 27i + 15i^2$

$15i^2 + 27i - 6$

How do you simplify (6 + 3i)(-1 + 5i)(6 + 3i)(-1 + 5i)?