Question

.solve it fast please​​

Answer 1

it lies in the second quadrant

Answer 2

Answer:

Second quadrant

Step-by-step explanation:

Given :

$\mathrm{Point \ \dfrac{1 + 2i}{1-i}}$

To find :

the Quadrant where lies the given point

Solution :

$\longmapsto \mathrm{\dfrac{1 + 2i}{1-i}}$

Multiply and divide by (1 + i)

$\implies \mathrm{\dfrac{1 + 2i}{1-i}\times \dfrac{1+i}{1+i}}$

$\implies \mathrm{\dfrac{(1 + 2i)(1+i)}{1+1}}$       ------ We know that, √-1 = i

$\implies \mathrm{\dfrac{1(1+i) + 2i(1+i)}{2}}$

$\implies \mathrm{\dfrac{1+i + 2i-2}{2}}$

$\implies \mathrm{\dfrac{-1+3i}{2}}$

So it is (-1/2, 3/2)

We know that, (-x, y) lies in second quadrant

So,

$\implies \mathrm{\dfrac{-1+3i}{2}} \ also \ lies \ in\ second\ quadrant$

Hope it helps!!