Given that $z=\sqrt{3}-\mathbf{i}$ and $w=-1+\sqrt{3}\mathbf{i}$, sketch in a single Argand

Question

Given that $z=\sqrt{3}-\mathbf{i}$ and $w=-1+\sqrt{3}\mathbf{i}$, sketch in a single Argand diagram $z^*$, $-w$, $3w$, $z+w$, showing clearly, their relationship.

Accepted Answer

$\text{(a)}\ z^*=\sqrt{3}+\mathbf{i}$ $\text{(b)}\ -w=1-\sqrt{3}\mathbf{i}$ $\text{(c)}\ 3w=-3+3\sqrt{3}\mathbf{i}$ $\text{(d)}\ z+w=(\sqrt{3}-1)+(\sqrt{3}-1)\mathbf{i}$

Complex Numbers - Geometrical Transformations of Complex Numbers

Complex Numbers - Geometrical Transformations of Complex Numbers

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