Let z=x+iy𝑧=𝑥+𝑖𝑦 and a point P𝑃 represent z𝑧 in the Argand plane. If the real part of z−1z+i𝑧-1𝑧+𝑖 is 1,1, then a point that lies on the locus of P𝑃 is

Question

Let z=x+iy𝑧=𝑥+𝑖𝑦 and a point P𝑃 represent z𝑧 in the Argand plane. If the real part of z−1z+i𝑧-1𝑧+𝑖 is 1,1, then a point that lies on the locus of P𝑃 is
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Solution 1

The given condition is that the real part of (z - 1)/(z + i) is 1.

Let's write z as x + iy and substitute it into the equation:

Real[(x + iy - 1) / (x + iy + i)] = 1

This simplifies to:

Real[((x - 1) + iy) / (x + (y + 1)i)] = 1

The real part of a complex number a + bi is a. So, we can separate Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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