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Question

Find the point of intersection of the curves arg(z3i)=3π/4 and arg(2z+12i)=π/4

A
1+3i
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B
3+i
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C
1-i
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D
given curves do not intersect.
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Solution

The correct option is D given curves do not intersect.
Give loci are as follows:
arg(z3i)=3π4
which is a ray that starts from 3i and makes an angle an 3π/4 with the positive real axis as shown in Fig. 3.18
arg(2z+12i)=π4
or arg[2(z+12i)]=π4
or arg2+arg[z(π4)]=π4
or 0+arg[z(12+i)]π4
or arg[z(12+i)]=π4
This is a ray that starts from point -1/2 + i and makes an angle π/4 with the positive real axis as shown in the figure. From the figure, it is obvious that the system of equation has no solution.

Ans: D
251741_133300_ans.png

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