here is how you find the additive inverse of a complex number, in general: let's say we have our complex number z a + bi we need to find some other complex number w x + yi with z + w 0 remember that 0 0 + 0i. so if z + w 0, what we are saying is: a + bi + x + yi 0 + 0i so we add the two, to get (a + x) + (b + y)i 0 + 0i for the two to be EQUAL, a + x 0, b + y 0 (two complex numbers are the same if and only if their real and imaginary parts are the same). from a + x 0, we know that x -a from b + y 0, we know that y -b so -z w -a - bi to get the negative, change the sign of the real and imaginary parts. so -(-8 - 5i) 8 + 5i
The additive inverse is whatever you can add to it to make it not affect an equation, in other words, to produce 0. 8 + 5i is your answer.
Let x additive inverse. -8 - 5i + x 0 x 8 + 5i
