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(1 + 2i)/(1 - i) lies in the
- a)I quadrant
- b)II quadrant
- c)III quadrant
- d)IV quadrant
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
(1 + 2i)/(1 - i) lies in thea)I quadrantb)II quadrantc)III quadrantd)I...
Explanation:
Given Expression:
(1 + 2i)/(1 - i)
Converting the denominator to standard form:
1 - i = 1 - i * (1 + i) / (1 + i)
= 1 - i - i + i^2 / (1 + i)
= 1 - i - i - 1 / (1 + i)
= -2i / (1 + i)
Substitute the denominator back into the expression:
(1 + 2i) / (-2i) * (1 + i)
= (1 + 2i) * (1 + i) / -2i
= 1 + i + 2i + 2i^2 / -2i
= 1 + 3i - 2 / -2i
= -1/2 - 3/2i
Plotting on the Complex Plane:
The real part is -1/2 and the imaginary part is -3/2. This point lies in the II quadrant of the complex plane.
Therefore, the given expression (1 + 2i)/(1 - i) lies in the II quadrant.
Given Expression:
(1 + 2i)/(1 - i)
Converting the denominator to standard form:
1 - i = 1 - i * (1 + i) / (1 + i)
= 1 - i - i + i^2 / (1 + i)
= 1 - i - i - 1 / (1 + i)
= -2i / (1 + i)
Substitute the denominator back into the expression:
(1 + 2i) / (-2i) * (1 + i)
= (1 + 2i) * (1 + i) / -2i
= 1 + i + 2i + 2i^2 / -2i
= 1 + 3i - 2 / -2i
= -1/2 - 3/2i
Plotting on the Complex Plane:
The real part is -1/2 and the imaginary part is -3/2. This point lies in the II quadrant of the complex plane.
Therefore, the given expression (1 + 2i)/(1 - i) lies in the II quadrant.
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(1 + 2i)/(1 - i) lies in thea)I quadrantb)II quadrantc)III quadrantd)IV quadrantCorrect answer is option 'B'. Can you explain this answer?
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