Question

Additive inverse of \[ - 1 - i\] is
A. 0+0i
B.1-i
C.1+i
D. None of these.

Answer 1

Hint: The sum of a number and its additive inverse is zero. If the number is real, its additive inverse is simply the negative of that number but the given number is a complex number. So we have to first assume a complex number $x + iy$ then we will equate the sum of given complex number and its additive inverse to zero.

Complete step-by-step answer:
In the given question, we have to find the additive inverse of a complex number -1-i
Let the given complex number be $x + iy$ and the required additive inverse be $a + ib$ .
Now, we know that the sum of the number and its additive inverse is zero. So the sum of the given complex number and its additive inverse will be zero.
$
  \therefore x + iy + a + ib = 0 \\
   \Rightarrow x + iy = - a - ib \\
 $
Now, on equating the real and imaginary part, we get:
$
  x = - a \\
   \Rightarrow a = - x \\
$ and $
  y = - b \\
   \Rightarrow b = - y \\
 $
But we know that $x + iy = - 1 - i$
$a = - ( - 1) = 1$
$b = - ( - 1) = 1$ .
Therefore the additive inverse of the given complex number is 1+i.
So, option C is correct.

Note: In this type of question, you should know that the sum of a number and its additive inverse is zero. Since the given number is a complex number so you have to assume a new complex number and then add both of the complex numbers to zero. Finally equate the real and imaginary part to get the additive inverse.