Match the following List I with List II (for z = x + i y , x , y )

Question

Match the following List I with List II (for $z = x + i y, x, y \in ℝ$ )

	List I		List II
P)	Area of the triangle formed by the complex numbers $z, ω z, z + ω z$ is $16 \sqrt{3}$ , then $\| z \|$ is (where $ω$ is a non-real cube root of unity)	1)	4
Q)	Area of the locus of $z$ , if $\| R e z \|$ $+$ $\| I m z \|$ $= 3$	2)	8
R)	If $\| z + \frac{6}{z} \|$ $= 5$ then the maximum of $\| z \|$ is	3)	6
S)	Number of complex numbers $' z'$ which satisfy $z^{2} = \bar{z}$ is (are)	4)	18

Smart Achievers · Accepted Answer

(2)

$A) Area of triangle = \frac{\sqrt{3}}{4} | z |^{2} = 16 \sqrt{3} \Rightarrow | z | = 8$

$B) Required area = 4 \times \frac{1}{2} \times 3^{2}$

$C) | z | - \frac{6}{| z |} \leq 5 \Rightarrow | z |^{2} - 5 | z | - 6 \leq 0 \Rightarrow | z | \leq 6$

$D) Conceptual$

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