Question

How do you simplify: (–7i +8i – 3i)?

Answer 1

Hint: Assume the given expression as ‘E’. Now, take ‘i’ common from all the three terms and use simple arithmetic operations: addition or subtraction, whichever needed, to simplify the expression. First add the negative terms by taking minus sign common and then add the result with the positive number 8 to get the answer.

Complete step by step solution:
Here, we have been provided with the expression: (–7i +8i – 3i) and we are asked to simplify it.
Now, let us assume the given expression as E, so we have,
$\Rightarrow $ E = –7i +8i – 3i
In the above expression we can see that there are three terms in which all the terms contain the letter ‘i’ which may be a variable or the notation for the imaginary number $\sqrt{-1}$ that is not mentioned here. So, we can assume anything. Here, we have to take ‘i’ common from each term to simplify the expression. So, we have,
$\Rightarrow $ E = i (–7 + 8 – 3)
The above expression can be written as,
$\Rightarrow $ E = i [–(7 + 3) + 8]
Therefore, on simplifying we get,
$\Rightarrow $ E = i [–10 + 8]
$\Rightarrow $ E = i (–2)
$\Rightarrow $ E = –2i
Hence, the simplified value of the given expression is: (–2i) which is our answer.

Note: One may note that here we have no information regarding the letter ’i’, if you will consider the question from the topic complex number then ‘i’ will be considered as an imaginary number $\sqrt{-1}$ and if you will consider the question from the topic linear algebra then it will be considered as a variable which may be any real number. However, whatever you may assume you will get the answer –2i and to simplify further we would require more information about ‘i’.