If the amplitude of z - 1 - 2 i is π 3 , then the locus of z is

Question

If the amplitude of z - 1 - 2 i is π 3 , then the locus of z is, y = 3 x + ( 2 - 3 ), y = 3 x - 3, x = 3 y + ( 2 - 3 ), y = 3 x + 2

MARKS App · Accepted Answer

Amplitude of ( z - 1 - 2 i ) is π 3 ( x + i y - 2 i - 1 ) = ( x - 1 ) + i ( y - 2 ) Now tan π 3 = y - 2 x - 1 ⇒ 3 = ± y - 2 x - 1 ⇒ 3 x - 3 = y - 2 3 x + ( 2 - 3 ) = y … i and 3 = - y - 2 x - 1 3 x - 3 = - y + 2 y + 3 x - 2 + 3 = 0 … ii

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