Question

How do you simplify $ (3 + 3i) - (4 - 3i) $ ?

Answer 1

Hint: To simplify this question , we need to solve it step by step . We should know that we can apply operations only on the like terms . We cannot perform calculations on different terms . In our given question , there are two different categories of the term in our question , that is we have two constants and two variables making up an algebraic expression . We will first solve the parentheses but there are unlike terms we cannot calculate them so we will just open the brackets and try to simplify them with the terms outside the brackets . Here 3i and -3i are like terms and the constant alone cannot be used in any operation . But here we have two constants so we can apply operations on it and simplify it . Following this method can result in the required solution.

Complete step by step solution:
In order to solve the expression , we should know the following things –
Like terms are the terms which have the same variables with the same power . And opposite to these are called Unlike terms which do not have variables with the same powers in common .
Here 3i and -3i are like terms , so we can apply additional operations on the terms . Also , the constants 3 and 4 in the question can be calculated together . If No other constant is present in the Question other than a single constant then we cannot apply any operation on that and it will remain as it is .
We can solve it in this way =>
 $ (3 + 3i) - (4 - 3i) $
Whenever there is any minus sign before the parentheses , while opening the parentheses we need to change the sign of the terms inside the parentheses as the numbers inside the parentheses get multiplied by -1 .
 $ (3 + 3i) - 4 + 3i $
Separate and Calculate the like terms .
 $ \Rightarrow 3i + 3i + 3 - 4 $
 $ \Rightarrow 6i - 1 $
We cannot take any thing common from the expression so ,
Therefore , the final answer to this question is $ 6i - 1 $ .
So, the correct answer is “ $ 6i - 1 $ ”.

Note: In like terms The Coefficients can be different but should have the same variable with the same power .
For example – 3x and 2x ,they are having different coefficients 2 and 3 but have common variable ‘ x’ , so these are like terms .
Keep in mind that whenever there is any minus sign before the parentheses , while opening the parentheses we need to change the sign of the terms inside the parentheses as the numbers inside the parentheses get multiplied by -1 .