AP EAMCET · Maths · Complex Number
In Argand plane, the quadrant in which \(\frac{1+2 i}{1-i}\) lies is
- A First
- B Second
- C Third
- D Fourth
Answer & Solution
Correct Answer
(B) Second
Step-by-step Solution
Detailed explanation
\(\frac{1+2 i}{1-i} = \frac{(1+2i)(1+i)}{(1-i)(1+i)}\) \(= \frac{1+i+2i+2i^2}{1-i^2}\) \(= \frac{1+3i-2}{1-(-1)}\) \(= \frac{-1+3i}{2}\) \(= -\frac{1}{2} + \frac{3}{2}i\) Real part \((x = -\frac{1}{2})\) is negative, imaginary part \((y = \frac{3}{2})\) is positive. The complex…
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