Question
Download Solution PDFIf z = x + iy, where i = √-1, then what does the equations zz̅ + ∣z∣2 + 4(z + z̅) - 48 = 0 represent?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
z = a + ib
Equation of circle: (x - h)2 + (y - k)2 = r2
Where (h,k) is the coordinates of center of the circle and r is the radius.
Calculation:
we have
(x + iy)(x - iy) + x2 + y2 + 4(x + iy + x - iy) - 48 = 0
⇒ x2 + y2 + x2 + y2 + 4 × 2x - 48 = 0
⇒ 2(x2 + y2) + 8x - 48 = 0
⇒ x2 + y2 + 4x - 24 = 0
⇒ (x + 2)2 + (y - 0)2 =
Since, the above equation is similar to (x - h)2 + (y - k)2 = r2
∴ The given equation represent a circle.
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