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

Question

Eli Assouline · Accepted Answer

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#

Kennedy Adams · Answer

undefined To simplify the expression $(6 + 3i)(-1 + 5i)$, you can use the distributive property and then combine like terms.

First, multiply each term in the first parentheses by each term in the second parentheses:

$(6)(-1) + (6)(5i) + (3i)(-1) + (3i)(5i)$

This simplifies to:

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

Next, combine like terms:

$-6 - 30i - 3i + 15(-1)$

Finally, simplify:

$-6 - 30i - 3i - 15$

$-21 - 33i$