{"@context":"https://schema.org/","@type":"Quiz","name":"

Product of a complex number with its own conjugate is a

","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"NET"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"NET","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/product-of-a-complex-number-with-its-own-conjugate-is-a"}],"about":{"@type":"Thing","name":"NET, NUST Entry Test, Mathematics, Number System, Quiz"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["NET","NUST Entry Test","Mathematics","Number System","Quiz"],"name":"

Product of a complex number with its own conjugate is a

","comment":{"@type":"Comment","text":"

Given a complex number $a+bi$, its conjugate $a-bi$ is obtained by changing the sign of the imaginary part. The product of a complex number and its conjugate is given as:

$(a+bi)(a-bi)$

$=(a)^{2}-(bi)^{2}$

$=a^{2}-b^{2}(i)^{2}$

$=a^{2}-b^{2}(-1)$ $\\because i^{2}=-1$

$=a^{2}+b^{2}$

Therefore the product of a complex number and its conjugate is a purely real number.

"},"encodingFormat":"text/markdown","text":"

Product of a complex number with its own conjugate is a

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

Prime number

"},{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

Imaginary number

"},{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

Real and imaginary number

"}],"acceptedAnswer":{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

Real number

","comment":{"@type":"Comment","text":"

Given a complex number $a+bi$, its conjugate $a-bi$ is obtained by changing the sign of the imaginary part. The product of a complex number and its conjugate is given as:

$(a+bi)(a-bi)$

$=(a)^{2}-(bi)^{2}$

$=a^{2}-b^{2}(i)^{2}$

$=a^{2}-b^{2}(-1)$ $\\because i^{2}=-1$

$=a^{2}+b^{2}$

Therefore the product of a complex number and its conjugate is a purely real number.

"},"answerExplanation":{"@type":"Comment","text":"

Given a complex number $a+bi$, its conjugate $a-bi$ is obtained by changing the sign of the imaginary part. The product of a complex number and its conjugate is given as:

$(a+bi)(a-bi)$

$=(a)^{2}-(bi)^{2}$

$=a^{2}-b^{2}(i)^{2}$

$=a^{2}-b^{2}(-1)$ $\\because i^{2}=-1$

$=a^{2}+b^{2}$

Therefore the product of a complex number and its conjugate is a purely real number.

"}}},"url":"https://classnotes.xyz/mcqs/product-of-a-complex-number-with-its-own-conjugate-is-a"}