Question

Rewrite each expression as a polynomial in standard form.a)(x+i)(x-i)b)(x+5i)(x-5i)

Answer 1

Answer:

a) x² +1

b) x² +25

Step-by-step explanation:

a) (x+i)(x− i)

   = x² - ( i ) x + ( i ) x - ( i)²

   = x² -  i²                       ∵ i² = -1

   = x² -  (-1)

   = x² +1

b) (x+5 i)(x− 5i)

 = x² - ( 5 i ) x + ( 5 i ) x - ( 5 i)²

   = x² - 25 i²                       ∵ i² = -1

   = x² -  25(-1)

   = x² +25

we can also solve

using identity

   (a + b)(a - b) = a² - b²

   = (x+5 i)(x− 5i)    

   = x² - (5 i)²

   = x² - 25 i²

   = x² +25