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Given z1 = √3 + i√3 and z2 = √3 + i, determine the quadrant in which the complex number z1/z2 lies.

1. I
2. II
3. III
4. IV

Correct answer: I

Solution

z1/z2 = (sqrt3 + i sqrt3)/(sqrt3 + i). Multiplying by the conjugate gives a positive real part (~1.18) and positive imaginary part (~0.32), so the quotient lies in Quadrant I.

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