Let O be the origin and A be the point ${z_1} = 1 + 2i$. If B is the point ${z_2}$, ${\mathop{\rm Re}\nolimits} ({z_2}) < 0$, such that OAB is a right angled isosceles triangle with OB as hypotenuse, then which of the following is NOT true?

Question

$\arg {z_2} = \pi - {\tan ^{ - 1}}3$

$\arg ({z_1} - 2{z_2}) = - {\tan ^{ - 1}}{4 \over 3}$

$|{z_2}| = \sqrt {10} $

$|2{z_1} - {z_2}| = 5$

Solution

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