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Definition of Functions

if z= x+iy ...

Question

if $z = x + i y$ satisfies amp $(z - 1)$ = amp $(z + 3 i)$ then the value of $(x - 1) : y$ is equal to

2 : 1

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1 : 3

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- 1 : 3

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None of these

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Solution

The correct option is D $1 : 3$
$z - 1 = w = (x - 1) + i y$ ...(i)
$z + 3 i = m = x + i (y + 3)$ ...(ii)
Now
$t a n (w) = t a n (m)$
Therefore
$\frac{y}{x - 1} = \frac{y + 3}{x}$
$x y = x y + 3 x - y - 3$
$3 (x - 1) = y$
$\frac{x - 1}{y} = \frac{1}{3}$
$(x - 1) : y = 1 : 3$
Hence, option 'B' is correct.

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