Question

Find roots of the equation Z ²-1=0,
where Z=X+iY​

Answer 1

The roots of the equation Z² - 1 = 0 are Z = -1 and Z = 1, with X and Y representing the real and imaginary parts of the complex number Z, respectively. Both roots are real numbers with Y = 0.

Step-by-step explanation:

To find the roots of the quadratic equation Z ² - 1 = 0, where Z is a complex number of the form Z = X + iY, we can rewrite the equation as (Z + 1)(Z - 1) = 0.

This implies that Z + 1 = 0 or Z - 1 = 0. Therefore, the roots of the equation are Z = -1 and Z = 1.

Since there is no imaginary part in the roots, this means that both X and Y are real numbers, with X = -1, Y = 0 for the first root, and X = 1, Y = 0 for the second root.