If 1 0 0 1 A And (3 I + 4 A) (3 I 4 A) = X2i Then The Value(s) X Is/are

2 min read Jun 26, 2024
If 1 0 0 1 A And (3 I + 4 A) (3 I 4 A) = X2i Then The Value(s) X Is/are

Solving the Equation:

Given the equation:

(1 + 0) + (0 + 1) = A and (3i + 4a) (3i - 4a) = x^2i

We are asked to find the value(s) of x.

Step 1: Simplify the first equation

The first equation can be simplified as:

2 = A

So, the value of A is 2.

Step 2: Expand the second equation

Using the distributive property, we can expand the second equation as:

(3i + 4a) (3i - 4a) = 9i^2 - 16a^2 = x^2i

Step 3: Equate the imaginary and real parts

Since the equation is equal to x^2i, we can equate the imaginary and real parts separately.

  • Imaginary part: 9i^2 = x^2i
  • Real part: -16a^2 = 0

Step 4: Solve for x

From the imaginary part, we can see that:

9i^2 = x^2i

Since i^2 = -1, we can rewrite the equation as:

-9 = x^2

Taking the square root of both sides, we get:

x = ±√9 = ±3

Answer:

Therefore, the value(s) of x are x = 3 or x = -3.