Question

If x= 3+4i and y= 3-4i, then find the value of X² + Y²

Answer 1

Complex numbers :

  • A complex number is of the form (a + ib), where both a and b are real numbers and i is the square root value of (- 1).

  • Any real number can be expressed as a complex number.

  • The set of complex number is the superset of all others sets like, Real numbers, Natural numbers.

  • Two  numbers (a + ib) and (a - ib) are called conjugate complex numbers, and its product is always a real number.

Given data is

x = 3 + 4i and y = 3 - 4i

Solution :

Now, x² + y²

 = (3 + 4i)² + (3 - 4i)²

 = 9 + 24i + 16i² + 9 - 24i + 16i²

{ identity rule : (a + b)² = a² + 2ab + b² }

 = 18 + 32i²

 = 18 + 32 (- 1), since i² = - 1

 = 18 - 32

 = - 14

Answer 2

Answer:

x² + y² = -14

Step-by-step explanation:

We know that,

⇒ x² + y² = ( x + y )² - 2xy

Here,

x = 3 + 4i and y = 3 - 4i

Substituting the values we get,

⇒ x² + y² = ( 3 + 4i + 3 - 4i )² - 2 ( 3 + 4i ) ( 3 - 4i )

⇒ x² + y² = ( 6 )² - 2 ( 3² - (4i)² )

⇒ x² + y² = 36 - 2 ( 9 - ( 16 × -1 ) )  [ Since i² = -1 ]

⇒ x² + y² = 36 - 2 ( 9 + 16 )

⇒ x² + y² = 36 - 2 ( 25 )

⇒ x² + y² = 36 - 50

⇒ x² + y² = -14

This is the required answer.

Hope it helped !!

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