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The locus in the complex plane described by the equation Re 1 z = 1 4 is a
- a)Circle with radius 1
- b)Circle with radius 2
- c)Straight line not passing through origin
- d)Straight line passing through origin
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The locus in the complex plane described by the equation Re 1 z = 1 4 ...
Let z=x+iy
1/z =1/x+iy
re(1/z)=x/
√x^2+y^2
and it is equal to 1/4
solving we get equation of a circle and u also can get radius
1/z =1/x+iy
re(1/z)=x/
√x^2+y^2
and it is equal to 1/4
solving we get equation of a circle and u also can get radius
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Community Answer
The locus in the complex plane described by the equation Re 1 z = 1 4 ...
Understanding the Equation
To solve the equation Re(1/z) = 1/4, we first need to express the complex number z in a suitable form. Let z = x + iy, where x and y are real numbers.
Finding Re(1/z)
1. Calculate 1/z:
- 1/z = 1/(x + iy) = (x - iy)/(x^2 + y^2)
- This gives us Re(1/z) = x/(x^2 + y^2).
2. Setting the equation:
- From the given equation, we have x/(x^2 + y^2) = 1/4.
Rearranging the Equation
- Rearranging gives us:
- 4x = x^2 + y^2
- This can be rearranged to:
- x^2 - 4x + y^2 = 0.
Completing the Square
- We complete the square for the x terms:
- (x^2 - 4x + 4) + y^2 = 4
- This simplifies to:
- (x - 2)^2 + y^2 = 4.
Identifying the Locus
- The equation (x - 2)^2 + y^2 = 4 represents a circle:
- Center: (2, 0)
- Radius: 2.
Conclusion
Thus, the locus described by the equation Re(1/z) = 1/4 is indeed a circle with a radius of 2. Therefore, the correct answer is option 'B'.
To solve the equation Re(1/z) = 1/4, we first need to express the complex number z in a suitable form. Let z = x + iy, where x and y are real numbers.
Finding Re(1/z)
1. Calculate 1/z:
- 1/z = 1/(x + iy) = (x - iy)/(x^2 + y^2)
- This gives us Re(1/z) = x/(x^2 + y^2).
2. Setting the equation:
- From the given equation, we have x/(x^2 + y^2) = 1/4.
Rearranging the Equation
- Rearranging gives us:
- 4x = x^2 + y^2
- This can be rearranged to:
- x^2 - 4x + y^2 = 0.
Completing the Square
- We complete the square for the x terms:
- (x^2 - 4x + 4) + y^2 = 4
- This simplifies to:
- (x - 2)^2 + y^2 = 4.
Identifying the Locus
- The equation (x - 2)^2 + y^2 = 4 represents a circle:
- Center: (2, 0)
- Radius: 2.
Conclusion
Thus, the locus described by the equation Re(1/z) = 1/4 is indeed a circle with a radius of 2. Therefore, the correct answer is option 'B'.
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The locus in the complex plane described by the equation Re 1 z = 1 4 is aa)Circle with radius 1b)Circle with radius 2c)Straight line not passing through origind)Straight line passing through originCorrect answer is option 'B'. Can you explain this answer? for JEE 2026 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The locus in the complex plane described by the equation Re 1 z = 1 4 is aa)Circle with radius 1b)Circle with radius 2c)Straight line not passing through origind)Straight line passing through originCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The locus in the complex plane described by the equation Re 1 z = 1 4 is aa)Circle with radius 1b)Circle with radius 2c)Straight line not passing through origind)Straight line passing through originCorrect answer is option 'B'. Can you explain this answer?.
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