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MathsHardMCQ2024 ยท 01 Feb Shift 1

Q62.Let ๐‘†= ๐‘งโˆˆ๐ถ: ๐‘งโˆ’1 = 1 and โˆš2 โˆ’1๐‘ง+ ยฏ๐‘ง- ๐‘–๐‘ง- ยฏ๐‘ง= 2โˆš2. Let ๐‘ง1, ๐‘ง2 โˆˆ๐‘† be such that ๐‘ง1 = max๐‘งโˆˆ๐‘ ๐‘ง and 2 ๐‘ง2 = min๐‘งโˆˆ๐‘ ๐‘ง. Then โˆš2๐‘ง1 โˆ’๐‘ง2 equals: (1) 1 (2) 4 (3) 3 (4) 2

What This Question Tests

This question tests the ability to convert complex number conditions into geometric loci (circle and line), find their intersection points, and then determine the maximum and minimum modulus of these intersection points from the origin.

Concepts Tested

Locus of complex number (circle)Properties of complex numbers (z+zฬ„, z-zฬ„)Geometric interpretation of complex numbersMaximum and minimum modulus of a complex number

Formulas Used

|z-zโ‚€|=R (equation of circle)

z=x+iy => z+zฬ„=2x, z-zฬ„=2iy

|z|=โˆš(xยฒ+yยฒ)

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