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Question

Locus of complex number satisfying arg[(z5+4i)(z+32i)]=π4 is the arc of a circle

A
whose radius is 52 units
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B
whose radius is 5 units
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C
whose length (of arc) is 15π2 units
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D
whose centre is 25i
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Solution

The correct option is D whose centre is 25i

z0(3+2i)z0(54i)=BDADeiπ/2=i
z0+32i=iz05i4
z0=25i
Radius AD=|54i(25i)|
=|7+i|
=50=52 units
Length of arc =34 (perimeter of circle)
=34(2π×52)
=15π2 units

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