The equation z bar{z} + (2 - 3i) z + (2 + 3i) | vedclass

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(B) The general equation of a circle in the complex plane is given by $z \bar{z} + \bar{a} z + a \bar{z} + b = 0$, where the centre is $-a$ and the ra

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$3$

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(B) The general equation of a circle in the complex plane is given by $z \bar{z} + \bar{a} z + a \bar{z} + b = 0$, where the centre is $-a$ and the radius is $r = \sqrt{|a|^2 - b}$.Comparing the given equation $z \bar{z} + (2 - 3i) z + (2 + 3i) \bar{z} + 4 = 0$ with the general form, we have $a = 2 - 3i$ and $b = 4$.First, calculate $|a|^2 = |2 - 3i|^2 = 2^2 + (-3)^2 = 4 + 9 = 13$.Now, calculate the radius $r = \sqrt{|a|^2 - b} = \sqrt{13 - 4} = \sqrt{9} = 3$.Thus, the radius of the circle is $3 	ext{ units}$.

The equation $z \bar{z} + (2 - 3i) z + (2 + 3i) \bar{z} + 4 = 0$ represents a circle of radius (in $\text{ units}$)

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