Most Important Selected Qs for JEE AdvancedMathematicsComplex Number

If the complex number z satisfies the condition |z- 25 z |=24 , then which of the following is(are) correct?

Options

AMaximum distance of z from origin is 5
BMaximum distance of z from origin is 25
CMinimum distance of z from origin is 1
DMinimum distance of z from origin is 4

Correct answer

C. Minimum distance of z from origin is 1

Step-by-step solution

|| z₁|-| z₂|| |z₁+z₂ | || z |- 25 |z| | 24 -24 |z|- 25 |z| 24 aligned & (i) |z|^2-24|z|-25 0 & (|z|-25)(|z|+1) 0 |z| 25 & (ii) |z|^2+24|z|-25 0 (|z|+25)(|z|-1) 0 |z| 1 & 1 |z| 25 aligned

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