I.

⇒ |A| = x(5x + 1) – (–7)x

|A| = 5x² + 8x

II.

⇒ |A| = cosθ × cosθ – (–sinθ) x sinθ

|A| = cos²θ + sin²θ

|A| = 1

III.

⇒ |A| = cos15° × cos75° + sin15° x sin75°

|A| = cos(75 – 15)°

|A| = cos60°

|A| = 0.5.

IV.

⇒ |A| = (a + ib)( a – ib) – (c + id)( –c + id)

= (a + ib)( a – ib) + (c + id)( c – id)

= a² – i² b² + c² – i² d²

= a² – (–1)b² + c² – (–1)d²

= a² + b² + c² + d²