In the Argand plane,the quadrant in which fra | vedclass

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(B) To find the quadrant,we first simplify the complex number by multiplying the numerator and denominator by the conjugate of the denominator,which i

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(B) To find the quadrant,we first simplify the complex number by multiplying the numerator and denominator by the conjugate of the denominator,which is $1+i$: $\frac{1+2i}{1-i} 	imes \frac{1+i}{1+i} = \frac{1+i+2i+2i^2}{1^2-i^2}$ 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.

In the Argand plane,the quadrant in which $\frac{1+2i}{1-i}$ lies is:

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