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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 +...
To find the conjugate of a complex number, we simply change the sign of the imaginary part.
Given: (x + iy)(1 - 2i)
Step 1: Expand the expression
(x + iy)(1 - 2i) = x(1 - 2i) + iy(1 - 2i)
Step 2: Simplify the expression
= x - 2ix + iy - 2iy^2
= x - 2ix + iy - 2iy^2
Step 3: Rearrange the terms
= (x - 2iy^2) + i(y - 2x)
Step 4: Conjugate the expression
The conjugate of (x - 2iy^2) + i(y - 2x) is (x - 2iy^2) - i(y - 2x)
Therefore, the conjugate of (x + iy)(1 - 2i) is (x - 2iy^2) - i(y - 2x).
Comparing this with the given options, we can see that option C: x - iy = [(1 - i)/(1 - 2i)] matches the expression we obtained for the conjugate.
Hence, the correct answer is option C.
Given: (x + iy)(1 - 2i)
Step 1: Expand the expression
(x + iy)(1 - 2i) = x(1 - 2i) + iy(1 - 2i)
Step 2: Simplify the expression
= x - 2ix + iy - 2iy^2
= x - 2ix + iy - 2iy^2
Step 3: Rearrange the terms
= (x - 2iy^2) + i(y - 2x)
Step 4: Conjugate the expression
The conjugate of (x - 2iy^2) + i(y - 2x) is (x - 2iy^2) - i(y - 2x)
Therefore, the conjugate of (x + iy)(1 - 2i) is (x - 2iy^2) - i(y - 2x).
Comparing this with the given options, we can see that option C: x - iy = [(1 - i)/(1 - 2i)] matches the expression we obtained for the conjugate.
Hence, the correct answer is option C.
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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?
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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? 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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