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

1. arg z 2 = p – tan –1 3
2. arg (z 1 – 2z 2 ) = – tan –1 3 4
3. | z | 2 = 10
4. | z – z 2 | 2 1 = 5

Correct answer: | z – z 2 | 2 1 = 5

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