If the area of a triangle on the complex plane formed by the complex numbers $z,iz\text{ and }z+iz\text{ is }50\text{ sq.u.,then }\left|z\right|\text{ =}$

Clearly, it is a right-angled triangle

Thus,

Area of the given triangle

$\begin{array}{r}=\frac{1}{2}\times \left|z\right|\times \left|iz\right|\\ =\frac{1}{2}\times |z{|}^2\times |i|\\ =\frac{1}{2}\times |z{|}^2\end{array}$                                                

It is given that $\frac{1}{2}\times |z{|}^2=50$

$\begin{array}{r}\Rightarrow |z{|}^2=100\\ \Rightarrow \left|z\right|=10\end{array}$

Hence, the value of $\left|z\right|\text{ is }10$