Show that the area of the triangle on the argand diagram formed by ...

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Show that the area of the triangle on the argand diagram formed by the complex number \( z, i z \) and \( z+i z \)
\( \mathrm{P} \) is \( \frac{1}{2}|z|^{2} \).
\[
\text { (1986, } 2 \frac{1}{2} \text { M) }
\]
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