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If 1 + i is the conjugate of (x+iy)(1-2i), then
- a)x = 1/5
- b)y = 3/5
- c)x + iy = [(1-i)/(1-2i)]
- d)x - iy = [(1-i)/(1+2i)]
Correct answer is option 'C'. Can you explain this answer?
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If 1 + i is the conjugate of (x+iy)(1-2i), thena)x = 1/5b)y = 3/5c)x +...
Explanation:
Conjugate of a complex number:
When we have a complex number of the form a + bi, the conjugate of it is a - bi. In other words, the conjugate of a complex number changes the sign of the imaginary part.
Given equation:
Given that 1 + i is the conjugate of (x + iy)(1 - 2i).
Expand the product:
(x + iy)(1 - 2i) = x - 2ix + i^2y
= x - 2ix - y
= x - y - 2ix
Equating to the conjugate:
The conjugate of 1 + i is 1 - i. Therefore, we can equate x - y - 2ix to 1 - i.
Solving for x and y:
x - y = 1
-2x = -1
x = 1/2
Substitute x = 1/2 into x - y = 1
1/2 - y = 1
y = -1/2
Therefore, x = 1/2 and y = -1/2.
Converting to required form:
x + iy = 1/2 - i/2 = (1 - i)/2
Therefore, the correct option is c) x + iy = [(1 - i)/(2)].
Conjugate of a complex number:
When we have a complex number of the form a + bi, the conjugate of it is a - bi. In other words, the conjugate of a complex number changes the sign of the imaginary part.
Given equation:
Given that 1 + i is the conjugate of (x + iy)(1 - 2i).
Expand the product:
(x + iy)(1 - 2i) = x - 2ix + i^2y
= x - 2ix - y
= x - y - 2ix
Equating to the conjugate:
The conjugate of 1 + i is 1 - i. Therefore, we can equate x - y - 2ix to 1 - i.
Solving for x and y:
x - y = 1
-2x = -1
x = 1/2
Substitute x = 1/2 into x - y = 1
1/2 - y = 1
y = -1/2
Therefore, x = 1/2 and y = -1/2.
Converting to required form:
x + iy = 1/2 - i/2 = (1 - i)/2
Therefore, the correct option is c) x + iy = [(1 - i)/(2)].
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If 1 + i is the conjugate of (x+iy)(1-2i), thena)x = 1/5b)y = 3/5c)x + iy = [(1-i)/(1-2i)]d)x - iy = [(1-i)/(1+2i)]Correct answer is option 'C'. Can you explain this answer?
Question Description
If 1 + i is the conjugate of (x+iy)(1-2i), thena)x = 1/5b)y = 3/5c)x + iy = [(1-i)/(1-2i)]d)x - iy = [(1-i)/(1+2i)]Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If 1 + i is the conjugate of (x+iy)(1-2i), thena)x = 1/5b)y = 3/5c)x + iy = [(1-i)/(1-2i)]d)x - iy = [(1-i)/(1+2i)]Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 1 + i is the conjugate of (x+iy)(1-2i), thena)x = 1/5b)y = 3/5c)x + iy = [(1-i)/(1-2i)]d)x - iy = [(1-i)/(1+2i)]Correct answer is option 'C'. Can you explain this answer?.
If 1 + i is the conjugate of (x+iy)(1-2i), thena)x = 1/5b)y = 3/5c)x + iy = [(1-i)/(1-2i)]d)x - iy = [(1-i)/(1+2i)]Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If 1 + i is the conjugate of (x+iy)(1-2i), thena)x = 1/5b)y = 3/5c)x + iy = [(1-i)/(1-2i)]d)x - iy = [(1-i)/(1+2i)]Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 1 + i is the conjugate of (x+iy)(1-2i), thena)x = 1/5b)y = 3/5c)x + iy = [(1-i)/(1-2i)]d)x - iy = [(1-i)/(1+2i)]Correct answer is option 'C'. Can you explain this answer?.
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