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प्रश्न
Obtain the Cartesian form of the locus of z = x + iy in the following cases:
Im[(1 – i)z + 1] = 0
उत्तर
z = x + iy
Im[(1 – i)z + 1] = 0
⇒ Im [(1 – i)(z + iy) + 1] = 0
⇒ Im[x + iy – ix + y + 1] = 0
⇒ Im[(x + y + 1) + i(y – x)] = 0
Considering only the imaginary part
y – x = 0 ⇒ x = y
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