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Question

The greatest and least value of |z1+z2| If z1=24+7i and|z2|=6 are respectively

A
31,25
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B
25,19
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C
31,19
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D
none
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Solution

The correct option is C 31,19
|z2|=6 resresents a circle of radius 6 centred at (0,0).
z1=24+7i represents a point A(24,7).
Let a diameter through A meet the circle in points B and C, then AB is least and AC is greatest distance of A from the circle.
Clearly AO2=242+72=625
AO=25
Greatest distance =AB=AO+BO=256=31
Least distance =AB=AOBO=256=19

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