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Question: What will be the additive inverse of 1 – i A. 0 + 0i B. -1 - i C. -1 + i D. None of these...

What will be the additive inverse of 1 – i
A. 0 + 0i
B. -1 - i
C. -1 + i
D. None of these

Explanation

Solution

Hint : We can solve this question by separating the given term 1 - i into 2 parts as the two terms are different, that are 1 and –i. We should know the concept of additive inverse of a number. Additive identity is a value when added to an added number gives the same number. The additive identity in mathematics is equal to zero. The additive inverse of a number is defined as the number when added to the given number gives the additive identity. Mathematically, let us denote the additive inverse of a number x by y. The relation between x and y can be written as
x+y=additive identity=0x+y=\text{additive identity=0}

Complete step-by-step answer :
Subtracting by x, we get
x+y−x=0−x y=−x \begin{aligned} & x+y-x=0-x \\\ & y=-x \\\ \end{aligned}
Using this relation we can find the additive inverse of 1 and –i and add them to get the additive inverse of 1 – i.

In the question, we are asked to find the additive inverse of 1 – i. The terms 1 and –i are different because 1 is real and –I is imaginary. We can find the additive inverse of the two terms separately and add them eventually to get the answer.
The number 0 is denoted as the additive identity in mathematics because when we add 0 to any number, we get the same number. The additive inverse of a number is defined as the number which when added to the given number gives the value of additive identity.
Let us denote the additive inverse of a number x by y. The relation between x and y can be written as
x+y=additive identity=0x+y=\text{additive identity=0}
Subtracting by x, we get
x+y−x=0−x y=−x→(1) \begin{aligned} & x+y-x=0-x \\\ & y=-x\to \left( 1 \right) \\\ \end{aligned}
Consider the term x = 1. From equation-1, we can write the additive inverse of 1 as additive inverse=−(1)=−1\text{additive inverse}=-\left( 1 \right)=-1
Consider the term x = -i. From equation-1, we can write the additive inverse of -i as additive inverse=−(−i)=i\text{additive inverse}=-\left( -i \right)=i
The additive inverse of 1 – i will be the sum of the two additive inverses.
So, the correct answer is “Option C”.

Note : We can write the additive inverse of the given term by substituting it directly in the equation. That is
Required additive inverse = −(1−i)=−1−(−i)=−1+i-\left( 1-i \right)=-1-\left( -i \right)=-1+i . The answer tally with the solution.