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If $z_{1}$ and $z_{2}$ are two complex numbers and $a, b$ are two real numbers, then ${|a z_{1} - b z_{2}|}^{2} + {|b z_{1} + a z_{2}|}^{2}$ equals

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a2+b2z1z2

a2+b2z12+z22

2abz1z2

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detailed solution

Correct option is C

We haveaz1−bz22+bz1+az22=a2z12+b2z22−abz1z¯2−abz¯1z2+b2z12+a2z22+bazz¯2+baz¯1z2=a2+b2z12+z22

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If z1 and z2 are two complex numbers and a, b are two real numbers, then az1−bz22+bz1+az22 equals

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Ready to Test Your Skills?

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If $z_{1}$ and $z_{2}$ are two complex numbers and $a, b$ are two real numbers, then ${|a z_{1} - b z_{2}|}^{2} + {|b z_{1} + a z_{2}|}^{2}$ equals