Question

What is the additive inverse of $-1-i$?
(a) $0+0i$
(b) $1-i$
(c) $1+i$
(d) None of these

Answer 1

Hint: First of all understand the meaning of the term additive inverse of a number. Assume the additive inverse of the given expression as x. Now, add x and the given expression and equate it with 0. Solve for the value of x to get the answer.

Complete step by step solution:
Here we have been provided with the expression $-1-i$ and we are asked to find the additive inverse of this expression. First we need to understand the meaning of the terms ‘additive inverse’ of a number.
Now, in mathematics the term ‘additive inverse’ of a number is also called the opposite of a number. Additive inverse of a number (y) is defined as a number which when added to y gives the sum 0. For example: - the additive inverse of 5 is -5 because when we will add these two terms we will get the sum equal to 0.
Let us come to the question, assuming the additive inverse of $-1-i$ as x we must have the sum of x and $-1-i$ equal to 0 mathematically, so we get,
\[\begin{align}
  & \Rightarrow \left( -1-i \right)+x=0 \\
 & \Rightarrow -\left( 1+i \right)+x=0 \\
 & \therefore x=\left( 1+i \right) \\
\end{align}\]

So, the correct answer is “Option c”.

Note: Note that there is one more term known as the multiplicative inverse also called the reciprocal of a number. Multiplicative inverse of a number (y) is defined as the number which when multiplied to y gives 1. To find the additive inverse of any number just multiply it with -1 and to find the multiplicative inverse of any number divide 1 by that number.