For any two complex number z 1 and z 2 and any real numbers a and b -a z1-b z2-2-b z1-a z2-2-A- a2-b2z1- z2-B- a2-b2-z1-2-z2-2C- a2-b2-z1-2-z2-2D- None of these

The correct option is B |(az_1 bz_2)|^2 + nbsp; nbsp; |(bz_1 az_2)|^2 =a^2|z_1|^2+b^2|z_2|^2 2Re(ab)|z_1z_2|+b^2|z_1|^2+a^2|z_2|^2+2Re(ab)|z_2z_1| = (a^2 ...

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Byju's Answer

Standard XI

Mathematics

Properties of Cube Root of a Complex Number

For any two c...

Question

For any two complex number $z_{1}$ and $z_{2}$ and any

real numbers a and b; $| (a z_{1} - b z_{2}) |^{2}$ + $| (b z_{1} - a z_{2}) |^{2}$ =

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None of these

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Solution

The correct option is B

$| (a z_{1} - b z_{2}) |^{2}$ + $| (b z_{1} - a z_{2}) |^{2}$

= $a^{2}$ $| z_{1} |^{2}$ + $b^{2}$ $| z_{2} |^{2}$ -2Re(ab)| $z_{1}$ ${¯ ¯ ¯ z}_{2}$ |+ $b^{2}$ $| z_{1} |^{2}$ + $a^{2}$ $| z_{2} |^{2}$ +2Re(ab)| $z_{2}$ ${¯ ¯ ¯ z}_{1}$ |

= ( $a^{2}$ + $b^{2}$ )( $| z_{1} |^{2}$ +(|z_2|^2\))

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Similar questions

For any two complex numbers $z_{1} z_{2}$ and any two real numbers a and b $| a z_{1} - b z_{2} |^{2} + | b z_{1} + a z_{2} |^{2}$ =

Q. For any two complex number

z_{1}, z_{2}

and any two real numbers

a

and

b

| a z_{1} - b z_{2} |^{2} + | b z_{1} + a z_{2} |^{2} =

Q. For any two complex numbers

z_{1}, z_{2}

and any two real numbers

a, b

show that

| a z_{1} - b z_{2} |^{2} + | b z_{1} + a z_{2} |^{2} = (a^{2} + b^{2}) (| z_{1} |^{2} + | z_{2} |^{2})

Q. For any two complex numbers

z_{1}, z_{2}

and any real numbers a and b,

{| a z_{1} - b z_{2} |}_{1}^{2} + {| b z_{1} + a z_{2} |}_{1}^{2} = (a^{2} + b^{2}) ({| z_{1} |}_{1}^{2} + {| z_{2} |}_{2}^{2})

. If this is true enter 1, else enter 0.

State True and False

For any two complex numbers

z_{1}, z_{2}

and any real numbers a and b,

{| a z_{1} - b z_{2} |}_{1}^{2} + {| b z_{1} + a z_{2} |}_{1}^{2} = (a^{2} + b^{2}) [{| z_{1} |}_{1}^{2} + {| z_{2} |}_{2}^{2}] .

Type 1 for true and 0 for false

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For any two complex number z1 and z2 and any real numbers a and b; |(az1−bz2)|2 + |(bz1−az2)|2 =

The correct option is B |(az1−bz2)|2 + |(bz1−az2)|2 =a2|z1|2+b2|z2|2-2Re(ab)|z1¯¯¯z2|+b2|z1|2+a2|z2|2+2Re(ab)|z2¯¯¯z1| = (a2+b2)(|z1|2+(|z_2|^2\))

For any two complex number $z_{1}$ and $z_{2}$ and any

real numbers a and b; $| (a z_{1} - b z_{2}) |^{2}$ + $| (b z_{1} - a z_{2}) |^{2}$ =