Question

√7+√3i/√7-√3i+√7-√3i/√7+√3i is real​

Answer 1

Given: The expression √7+√3i/√7-√3i+√7-√3i/√7+√3i

To find: Whether the given expression is real or not?

Solution:

• Now we have given the expression as:

                 (√7+√3i/√7-√3i )+(√7-√3i/√7+√3i )

• Now rationalizing it, we get:

                 (√7+√3i/√7-√3i ) x(√7+√3i/√7+√3i ) + (√7-√3i/√7+√3i ) x (√7-√3i/√7-√3i )

• Now solving it further we get:

                 { (√7+√3i)^2 / (√7)^2-(√3i)^2 } + { (√7-√3i)^2 / (√7)^2-(√3i)^2 }

                 { 7 + 3i^2 + 2√21i } / 7 - 3i^2  } + { 7 + 3i^2 - 2√21i } / 7 - 3i^2  }

                 {  7 + 3i^2 + 2√21i  + 7 + 3i^2 - 2√21i / 7 - 3i^2  }

• Now we know that i^2 = -1, so applying it, we get:

                 {  7 + 3i^2 + 7 + 3i^2 / 7 - 3i^2  }

                 { 14 + 6(-1) / 7 - 3(-1)  }

                 8 / 10

                 4/5

Answer:

         So the value of given expression is 4/5 and it is real number.