Question

Find the additive inverse of $(1 - i)$

Answer 1

Here if we are asked to find the additive inverse of any number, we must have the knowledge that the additive inverse of the number is negative of itself. For example: Additive inverse of $a{\text{ is }} - a$ and of $1 + a{\text{ is }} - (1 + a)$. In simple words we mean by the additive inverse that we need to find the number that will be added to that so that the value after addition becomes zero. Hence it is negative of itself.

Complete step-by-step answer:
Here we are given to find the additive inverse of the complex number. Complex number is of the form $(a + ib)$ where the number $a$ is the real part of the complex number and $b$ is the imaginary part and $i$ is termed as iota whose value is $\sqrt { - 1}$
Now we need to know what the meaning of additive inverse is. Additive inverse of any number is the number that we need to add to it so that the value after addition vanishes or becomes zero. For example: If we have the number $8$ so we need to find the additive inverse of this number we need to find the number that will vanish it after addition. So let the additive inverse be $x$
So
$8 + x = 0 \\\ x = - 8 \\\$
Hence we can say that the negative of the number is the additive inverse of the number because the negative of the number when added to the positive of it the whole term will become zero.
Now we are given the complex number $(1 - i)$
Additive inverse will be therefore $- (1 - i) = - 1 + i$
Hence additive inverse is $- 1 + i$

Note: In order to take the multiplicative inverse of any number we need to find the number that when multiplies to that initial number makes the result unity which is $1$
For example: If we have the number $5$ then its multiplicative inverse will be $\dfrac{1}{5}$ as $5 \times \dfrac{1}{5} = 1$