How do you use the distributive property to simplify #5(6-3i)+3(i-8)#?

Answer 1

#6 - 12i#

I'm not sure if your #i# is just a variable or if it is an imaginary number, but either way that will not affect the simplified answer.

To simplify this, use the distributive property (shown below):

Following this image, we know that:
#color(blue)(5(6-3i) = (5 * 6) + (5 * -3i) = 30 - 15i)#
and
#color(blue)(3(i-8) = (3 * i) + (3 * -8) = 3i - 24)#

Now combine them:
#30 - 15i + 3i - 24#

Color-code the like terms:
#color(red)(30) quadcolor(green)(-quad15i) quadcolor(green)(+quad3i) quadcolor(red)(-quad24)#

Combine the like terms:
#6 - 12i#

Hope this helps!

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

[ 30 - 15i + 3i - 24 ] [ 6 - 12i ]

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7