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show that | |2 bar z + 5| ( sqrt 2 - 1)|...

show that `| |2 bar z + 5| ( sqrt 2 - 1)| = sqrt3 | 2z + 5|` , where z is a complex number.

Text Solution

Verified by Experts

As `|z|= | bar z|`
`|z_1z_2|= |z_1||z_2|`
`z= (2 bar z +5)( sqrt2 -i)`
`|z|= |2 bar z + 5||sqrt2 - i|`
`bar z = bar ((2 bar z + 5)(sqrt2 - i))`
`=bar ((2 bar z + 5)) * bar((sqrt2 - i))`
`= (2z+5)(sqrt2 +i)`
`|bar z|= |2z +5||sqrt2 +i|`
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