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MathsHardMCQ2022 ยท 29 Jul Shift 2

Q62.Let ๐‘†= ๐‘ง= ๐‘ฅ+ ๐‘–๐‘ฆ: ๐‘ง- 1 + ๐‘–โ‰ฅ๐‘ง, ๐‘ง< 2, ๐‘ง+ ๐‘–= ๐‘ง- 1. Then the set of all values of ๐‘ฅ, for which ๐‘ค= 2๐‘ฅ+ ๐‘–๐‘ฆโˆˆ๐‘† for some ๐‘ฆโˆˆโ„, is 1 1 1 (2) - (1) -โˆš2, 4 2โˆš2 โˆš2, (3) -โˆš2, 1 (4) - 1 1 2 โˆš2, 2โˆš2

What This Question Tests

This question defines a set S using multiple inequalities and an equality involving complex numbers, requiring a strong understanding of their geometric interpretation to find the region and then the possible values of x.

Concepts Tested

Distance in complex planeInequalities with complex numbersLocus of complex numbers

Formulas Used

|z - z1| >= |z - z2|

|z| < r

|z - z0| = r

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