The complex number frac{1+2i}{1-i} lies in | vedclass

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(A) To simplify the complex number,we multiply the numerator and denominator by the conjugate of the denominator $(1+i)$:$\frac{1+2i}{1-i} 	imes \fra

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second quadrant

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(A) To simplify the complex number,we multiply the numerator and denominator by the conjugate of the denominator $(1+i)$:$\frac{1+2i}{1-i} 	imes \frac{1+i}{1+i} = \frac{1+i+2i+2i^2}{1^2-i^2}$Since $i^2 = -1$,we have:$\frac{1+3i-2}{1-(-1)} = \frac{-1+3i}{2} = -\frac{1}{2} + \frac{3}{2}i$The real part is $-\frac{1}{2}$ (negative) and the imaginary part is $\frac{3}{2}$ (positive).$A$ complex number with a negative real part and a positive imaginary part lies in the second quadrant.

The complex number $\frac{1+2i}{1-i}$ lies in

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