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Mathematics Question on complex numbers

Let OO be the origin and AA be the point z1=1+2iz _1=1+2 i. If BB is the point z2,Re⁡(z2)<0z _2, \operatorname{Re}\left( z _2\right)<0, such that OABOAB is a right angled isosceles triangle with OBOB as hypotenuse, then which of the following is NOT true ?

A

arg⁡z2=π−tan⁡−13\arg z _2=\pi-\tan ^{-1} 3

B

arg⁡(z1−2z2)=−tan⁡−143\arg \left( z _1-2 z _2\right)=-\tan ^{-1} \frac{4}{3}

C

∣z2∣=10\left|z_2\right|=\sqrt{10}

D

∣2z1−z2∣=5\left|2 z_1-z_2\right|=5

Answer

∣2z1−z2∣=5\left|2 z_1-z_2\right|=5

Explanation

Solution

The correct option is (D): ∣2z1−z2∣=5\left|2 z_1-z_2\right|=5