How do you simplify #5-[(-3i+4)-2i]#?

Question

Aurora Arias · Accepted Answer

#5-[(-3i+4)-2i]=1+5i#

#5-[(-3i+4)-2i]#

= #5-[-3i+4-2i]#

= #5-[-5i+4]#

Now we have a negative sign outside brackets.

How do we interpret it?

There are two ways

(i) it is as if we are multiplying by #-1# and hence

#-[-5i+4]=-1xx[-5i+4]#

= #(-1)xx(-5i)+(-1)xx4=5i-4# or

(ii) using simple properties of negative numbers i.e. negative of a negative is positive and negative of a positive is negative and hence again #-{-5i+4]=5i-4#.

In any case, it means we change all the signs inside the brackets and above is equal to

#5+5i-4#

= #1+5i#

Jeremiah Andrews · Answer

undefined To simplify the expression $ 5 - [(-3i + 4) - 2i] $, follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). First, simplify the expression within the innermost parentheses by distributing the negative sign:

$$ -(-3i + 4) = 3i - 4 $$

Now, substitute this simplified expression back into the original expression:

$$ 5 - [3i - 4 - 2i] $$

Next, simplify the expression within the square brackets:

$$ 5 - (3i - 4 - 2i) = 5 - 3i + 4 + 2i $$

Combine like terms:

$$ 5 - 3i + 4 + 2i = (5 + 4) + (-3i + 2i) = 9 - i $$

Therefore, $ 5 - [(-3i + 4) - 2i] $ simplifies to $ 9 - i $.