Question

How do you solve `1= | z + 8|`?

Answer 1

`z=-7` or `z=-9`

Explanation:

`|k|` stands for absolute value of `k`, which is the numerical value of `k` sans its sign. So while the absolute value of `7` is `7`, absolute value of `|-7|` too is `7`.

In short, if `k` is positive `|k|=k`, but if `k` is negative `|k|=-k`.

Thus while `|7|=7`, `|-7|=-(-7)=7`.

Hence, as we have `1=|z+8|`

either `1=z+8`

i.e. `z+8=1` i.e. `z=1-8=-7`

or `1=-(z+8)`

i.e. `z+8=-1` i.e. `z=-1-8=-9`