Complex numbers

Algebra Level 4

A complex number z z satisfies the following two loci, arg ⁡ ( z − 3 ) = 4 5 ∘ \arg(z-3)=45^\circ and arg ⁡ ( z − 2 ) = 13 5 ∘ \arg(z-2)=135^\circ . Find the complex number z z .

None of these There is no such z z 2.5 − 0.5 i 2.5-0.5i − 2.5 + 0.5 i -2.5+0.5i

Indraneel Mukhopadhyaya by Indraneel Mukhopadhyaya , 22, India

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1 solution

Locus of arg(z-3)=45 degrees is a ray that passes through (3,0) and and makes 45 degrees with the positive X axis.Locus of arg(z-2)=135 degrees is a ray that passes through (2,0) and makes 135 degrees with the positive X axis.We can clearly see that the two rays do not intersect.Hence there exists no complex number that satisfies both the given loci

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