(b) If $z = x + iy$ is the additive inverse of $1 - i$, the $x + iy + (1 - i) = 0$ $\Rightarrow \ \ \ \ x + 1 = 0,\ \ \ y - 1 = 0$ $\Rightarrow \ \ \ x = - 1,\ \ \ y = 1$ Here required additive inverse is $- 1 + i$
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Ph.D. in Physics with 19+ years of teaching experience.