Question

Which is the additive inverse of the complex number -8+3i?

Answer 1

The additive inverse of a complex z is a complex number $-z,$ so that

$\mathsf{z+(-z)=-z+z=0+0i=0}$


Finding $-z:$

$\mathsf{z=-8+3i}\\\\\\ \mathsf{z+(-z)=0+0i}\\\\\ \mathsf{-8+3i+(-z)=0+0i}\\\\ \mathsf{-z=0+0i+8-3i}\\\\ \mathsf{-z=(0+8)+(0i-3i)}\\\\ \boxed{\begin{array}{c}\mathsf{-z=8-3i} \end{array}}\qquad\checkmark$


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I hope this helps.


Tags: complex number additive inverse opposite algebra