Question

If Z1=1+i and Z2, =1-i then Z1/Z2

Answer 1

Answer:

z1 = 1 + i and z2 = 1 - i

z1/z2 = (1+i) / (1-i)

= {(1+i) / (1-i)} * {(1+i) / (1-i)}

= (1+i)² / (1-i²)

= (1 +2i + i²) / (1 - (-1))

= (1 + 2i - 1)/(1+1)

= 2i/2

= i

Answer 2

Answer:

The value of $\frac{Z_1}{Z_2}$ = i

Step-by-step explanation:

Given,

$Z_1$ = 1+i

$Z_2$ = 1 -i

To find,

$\frac{Z_1}{Z_2}$

Solution:

$\frac{Z_1}{Z_2}$ = $\frac{1+i}{1-i}$

To simplify this complex number, we should multiply the numerator and denominator with the complex conjugate of the denominator.

The complex conjugate of the denominator = 1 +i

$\frac{Z_1}{Z_2}$ = $\frac{1+i}{1-i}$ .

= $\frac{1+i}{1-i} X \frac{1+i}{1+i}$

= $\frac{(1+i)^2}{(1+i)(1-i)}$

= $\frac{1^2+(i)^2 + 2i}{(1)^2-(i)^2}$(since i = $\sqrt{-1}$, i² = -1)

=$\frac{1+(-1) + 2i}{1-(-1)}$

= $\frac{2i}{2}$

= i

$\frac{Z_1}{Z_2}$ = i

∴The value of $\frac{Z_1}{Z_2}$ = i

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