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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?
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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.
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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?
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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?.
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