Question

Please i am a new member... i want to find i when (1+i)^2 = 1.44 . I need steps

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Answer 1

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step-by-step explanation:

Solution using a² - b² = (a + b) (a - b) identity :

Given that, (1 + i)² = 1.44

      ⇒ (1 + i)² - 1.44 = 0

      ⇒ (1 + i)² - 1.2² = 0

      ⇒ (1 + i + 1.2) (1 + i - 1.2) = 0

      ⇒ (i + 2.2) (i - 0.2) = 0

Either i + 2.2 = 0 or, i - 0.2 = 0

      ⇒ i = - 2.2 , 0.2 ,

which is the required solution.

Solution by taking squared root :

Given that, (1 + i)² = 1.44

      ⇒ 1 + i = ± √1.44

      ⇒ 1 + i = ± 1.2

Then, 1 + i = 1.2 and 1 + i = - 1.2

      ⇒ i = 0.2 , - 2.2 ,

which is the required solution.

Solution using middle term method :

Given that, (1 + i)² = 1.44

      ⇒ 1² + 2i + i² - 1.44 = 0

      ⇒ i² + 2i - 0.44 = 0

      ⇒ i² + 2.2i - 0.2i - 0.44 = 0

      ⇒ i (i + 2.2) - 0.2 (i + 2.2) = 0

      ⇒ (i + 2.2) (i - 0.2) = 0

Either i + 2.2 = 0 or, i - 0.2 = 0

      ⇒ i = - 2.2 , 0.2 ,

which is the required solution.

Identities :

  (a + b)² = a² + 2ab + b²

  a² - b² = (a + b) (a - b)