Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Assertion :The product of the real part of the roots of the eq

Question

Assertion :The product of the real part of the roots of the equation $z^{2} + 4 z + 4 i = 0$ and $2 - 22$
Reason :The roots of equation is given as $2 (- 1 \pm 42 e^{- i \frac{π}{8}})$ and then take the product of real part.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Assertion is correct but Reason is incorrect

Both Assertion and Reason are incorrect

Views: 2,324 students

Found 2 tutors discussing this question

Olivia Discussed

Assertion :The product of the real part of the roots of the equation

z^{2} + 4 z + 4 i = 0

and

2 - 22

Reason :The roots of equation is given as

2 (- 1 \pm 42 e^{- i \frac{π}{8}})

and then take the product of real part.

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

Reason: Roots of equation

z^{2} + 4 z + 4 i = 0

is given by

(z + 2)^{2} = 4 - 4 i = 4 (1 - i)

\Rightarrow {z - (- 2)}^{2} = 42 e^{- \frac{π}{4} i}

\Rightarrow z = - 2 \pm 2 (2^{\frac{1}{4}}) e^{- \frac{π}{8} i}

and product of real parts is

(2 - 22)

which shows that the reason is true.

Assertion: is true as the product of real parts of roots

= (- 2)^{2} {1 - 2 cos^{2} \frac{π}{8}}

= 4 ⎩ ⎨ ⎧ 1 - 2 (\frac{2 + 1}{2 2})^{2} ⎭ ⎬ ⎫ = 2 - 22

So assertion is derived from reason.

Was this solution helpful?

155

Report

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our maths tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	Assertion :The product of the real part of the roots of the equation $z^{2} + 4 z + 4 i = 0$ and $2 - 22$ Reason :The roots of equation is given as $2 (- 1 \pm 42 e^{- i \frac{π}{8}})$ and then take the product of real part.
Answer Type	Text solution:1
Upvotes	155