If z1,z2 are two complex numbers such that z1=z2=2 and z1+z2=3 than z1−z2 equals;

z1+z22+z1−z22=2z12+2z22⇒ 3+z1−z22=2(2)+2(2)⇒ z1−z22=5⇒z1−z2=5

If z1,z2 are two complex numbers such that z1=z2=2 and z1+z2=3 than z1−z2 equals;

z1+z22+z1−z22=2z12+2z22⇒ 3+z1−z22=2(2)+2(2)⇒ z1−z22=5⇒z1−z2=5

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If $z_{1}, z_{2}$ are two complex numbers such that $|z_{1}| =$ $|z_{2}| = \sqrt{2}$ and $|z_{1} + z_{2}| = \sqrt{3}$ than $|z_{1} - z_{2}|$ equals;

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$2 - \sqrt{2}$

$2 \sqrt{2}$

$\sqrt{5}$

answer is B.

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$\begin{array}{l} {|z_{1} + z_{2}|}^{2} + {|z_{1} - z_{2}|}^{2} = 2 {|z_{1}|}^{2} + 2 {|z_{2}|}^{2} \\ \Rightarrow 3 + {|z_{1} - z_{2}|}^{2} = 2 (2) + 2 (2) \\ \Rightarrow {|z_{1} - z_{2}|}^{2} = 5 \Rightarrow |z_{1} - z_{2}| = \sqrt{5} \end{array}$

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If z1,z2 are two complex numbers such that z1=z2=2 and z1+z2=3 than z1−z2 equals;

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If $z_{1}, z_{2}$ are two complex numbers such that $|z_{1}| =$ $|z_{2}| = \sqrt{2}$ and $|z_{1} + z_{2}| = \sqrt{3}$ than $|z_{1} - z_{2}|$ equals;