UPSC Exam > UPSC Questions > It's that is equal to X + iota by where I is ...
Start Learning for Free
It's that is equal to X + iota by where I is root -1 then what does the equation z into z + mod z square + 4 z plus z bracket minus 48 is equal to zero?
Most Upvoted Answer
It's that is equal to X + iota by where I is root -1 then what does th...
Given Equation:
It is given that z = X + iota, where iota is the square root of -1.
Explanation:
To solve the equation z(z + |z|^2 + 4z + z - 48) = 0, we can substitute z = X + iota into the equation and simplify it step by step.
Step 1:
Substitute z = X + iota into the equation:
(X + iota)((X + iota) + |X + iota|^2 + 4(X + iota) + (X + iota) - 48) = 0
Step 2:
Expand the equation and simplify:
(X + iota)(X + iota + |X + iota|^2 + 4X + 4iota + X + iota - 48) = 0
(X + iota)(X + iota + X^2 + 2iotaX - 1 + 4X + 4iota + X + iota - 48) = 0
(X + iota)(2X^2 + 6X + 6iota) = 0
Step 3:
Expand further:
2X^3 + 6X^2 + 6iotaX^2 + 6X^2 + 18X + 18iotaX = 0
2X^3 + 12X^2 + 18X + 6iotaX^2 + 18iotaX = 0
Step 4:
Separate real and imaginary parts:
2X^3 + 12X^2 + 18X = 0
6iotaX^2 + 18iotaX = 0
Step 5:
Solve the real part equation for X:
2X(X^2 + 6X + 9) = 0
2X(X + 3)^2 = 0
X = 0 or X = -3
Step 6:
Solve the imaginary part equation for X:
6iotaX(X + 3) = 0
Since iota is not equal to 0, X = 0 or X = -3
Conclusion:
Therefore, the solutions to the equation z(z + |z|^2 + 4z + z - 48) = 0 are X = 0 and X = -3.
It is given that z = X + iota, where iota is the square root of -1.
Explanation:
To solve the equation z(z + |z|^2 + 4z + z - 48) = 0, we can substitute z = X + iota into the equation and simplify it step by step.
Step 1:
Substitute z = X + iota into the equation:
(X + iota)((X + iota) + |X + iota|^2 + 4(X + iota) + (X + iota) - 48) = 0
Step 2:
Expand the equation and simplify:
(X + iota)(X + iota + |X + iota|^2 + 4X + 4iota + X + iota - 48) = 0
(X + iota)(X + iota + X^2 + 2iotaX - 1 + 4X + 4iota + X + iota - 48) = 0
(X + iota)(2X^2 + 6X + 6iota) = 0
Step 3:
Expand further:
2X^3 + 6X^2 + 6iotaX^2 + 6X^2 + 18X + 18iotaX = 0
2X^3 + 12X^2 + 18X + 6iotaX^2 + 18iotaX = 0
Step 4:
Separate real and imaginary parts:
2X^3 + 12X^2 + 18X = 0
6iotaX^2 + 18iotaX = 0
Step 5:
Solve the real part equation for X:
2X(X^2 + 6X + 9) = 0
2X(X + 3)^2 = 0
X = 0 or X = -3
Step 6:
Solve the imaginary part equation for X:
6iotaX(X + 3) = 0
Since iota is not equal to 0, X = 0 or X = -3
Conclusion:
Therefore, the solutions to the equation z(z + |z|^2 + 4z + z - 48) = 0 are X = 0 and X = -3.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Top Courses for UPSCView all
It's that is equal to X + iota by where I is root -1 then what does the equation z into z + mod z square + 4 z plus z bracket minus 48 is equal to zero?
Question Description
It's that is equal to X + iota by where I is root -1 then what does the equation z into z + mod z square + 4 z plus z bracket minus 48 is equal to zero? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about It's that is equal to X + iota by where I is root -1 then what does the equation z into z + mod z square + 4 z plus z bracket minus 48 is equal to zero? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for It's that is equal to X + iota by where I is root -1 then what does the equation z into z + mod z square + 4 z plus z bracket minus 48 is equal to zero?.
It's that is equal to X + iota by where I is root -1 then what does the equation z into z + mod z square + 4 z plus z bracket minus 48 is equal to zero? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about It's that is equal to X + iota by where I is root -1 then what does the equation z into z + mod z square + 4 z plus z bracket minus 48 is equal to zero? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for It's that is equal to X + iota by where I is root -1 then what does the equation z into z + mod z square + 4 z plus z bracket minus 48 is equal to zero?.
Solutions for It's that is equal to X + iota by where I is root -1 then what does the equation z into z + mod z square + 4 z plus z bracket minus 48 is equal to zero? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of It's that is equal to X + iota by where I is root -1 then what does the equation z into z + mod z square + 4 z plus z bracket minus 48 is equal to zero? defined & explained in the simplest way possible. Besides giving the explanation of
It's that is equal to X + iota by where I is root -1 then what does the equation z into z + mod z square + 4 z plus z bracket minus 48 is equal to zero?, a detailed solution for It's that is equal to X + iota by where I is root -1 then what does the equation z into z + mod z square + 4 z plus z bracket minus 48 is equal to zero? has been provided alongside types of It's that is equal to X + iota by where I is root -1 then what does the equation z into z + mod z square + 4 z plus z bracket minus 48 is equal to zero? theory, EduRev gives you an
ample number of questions to practice It's that is equal to X + iota by where I is root -1 then what does the equation z into z + mod z square + 4 z plus z bracket minus 48 is equal to zero? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup