Questions & Answers

Question

Answers

A. 0 + 0i

B. -1 - i

C. -1 + i

D. None of these

Answer
Verified

$ x+y=\text{additive identity=0} $

Subtracting by x, we get

$ \begin{align}

& x+y-x=0-x \\

& y=-x \\

\end{align} $

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=\text{additive identity=0} $

Subtracting by x, we get

$ \begin{align}

& x+y-x=0-x \\

& y=-x\to \left( 1 \right) \\

\end{align} $

Consider the term x = 1. From equation-1, we can write the additive inverse of 1 as $ \text{additive inverse}=-\left( 1 \right)=-1 $

Consider the term x = -i. From equation-1, we can write the additive inverse of -i as $ \text{additive inverse}=-\left( -i \right)=i $

The additive inverse of 1 – i will be the sum of the two additive inverses.

Required additive inverse = $ -\left( 1-i \right)=-1-\left( -i \right)=-1+i $ . The answer tally with the solution.

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