Match the expressions in List-I with their corresponding values/properties in List-II. List - I List - II (P) ∣ z 1 + z 2 ∣ 2 + ∣ z 1 − z 2 ∣ 2 (1) 2 Re ( z ) (Q) For a complex number z = x +

Question

Match the expressions in List-I with their corresponding values/properties in List-II.

List - I	List - II
(P) $∣ z_{1} + z_{2} ∣^{2} + ∣ z_{1} - z_{2} ∣^{2}$	(1) $2 Re (z)$
(Q) For a complex number $z = x + i y$ , the value of $z + \overset{z}{ˉ}$	(2) $0$
(R) For a purely imaginary number $z$ , the value of $z + \overset{z}{ˉ}$	(3) $2 (∣ z_{1} ∣^{2} + ∣ z_{2} ∣^{2})$
(S) For a complex number $z = x + i y$ , the value of $z - \overset{z}{ˉ}$	(4) $2 i Im (z)$

TestHub · Accepted Answer

For (P), using the parallelogram law, ∣ z 1 ​ + z 2 ​ ∣ 2 + ∣ z 1 ​ − z 2 ​ ∣ 2 = 2 ( ∣ z 1 ​ ∣ 2 + ∣ z 2 ​ ∣ 2 ) . For (Q), if z = x + i y , then z + z ˉ = ( x + i y ) + ( x − i y ) = 2 x = 2 Re ( z ) . For (R), if z is purely imaginary, z = i y for some real y . Thus, z + z ˉ = i y + ( − i y ) = 0 . For (S), if z = x + i y , then z − z ˉ = ( x + i y ) − ( x − i y ) = 2 i y = 2 i Im ( z ) .

Mathematics - Complex Number Question with Solution | TestHub

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