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  •   Modulus of 2 complex no's are 4 and 7 and modulus of sum of these complex numbers is 9, then <img alt="z_{1}\bar{z_{2}}+\bar{z_{1}}z_{2}=" src="http://entrancecorner.oncodec

The modulus of 2 complex numbers is 4 and 7, and the modulus of the sum of these complex numbers is 9, then z_{1}\bar{z_{2}}+\bar{z_{1}}z_{2}=

Answers (1)

best_answer

Given- $$ 
|z_{1}| = 4⇒z_{1}\bar{z_{1}}= 16
$$ 
$$ 
|z_{2}| = 7⇒z_{2}\bar{z_{2}}= 49
$$ 
$$
|z_{1} +z_{2}| = 9 ⇒|z_{1} +z_{2}| ^2 = 81
$$

To find- $$ 
z_{1}\bar{z_{2}}+\bar{z_{1}}z_{2}
$$ 

Solution- Using identity, $$
|z_{1} +z_{2}| ^2 = |z_{1}|^2 + |z_{2}|^2 + z_{1}\bar{z_{2}}+\bar{z_{1}}z_{2}
$$ 

Putting all values, $$
81 = 16+ 49 + z_{1}\bar{z_{2}}+\bar{z_{1}}z_{2}
$$ $$
z_{1}\bar{z_{2}}+\bar{z_{1}}z_{2} = 16
$$ 

Posted by

Saniya Khatri

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