Question

Show that 1+2i/3+4i*1-2i/3-4i is real​

Answer 1

Given: The term (1 + 2i)/(3 + 4i) x (1 - 2i)/(3 - 4i)

To find: Show that the given term is real.

Solution:

• Now we have given the term:

                  (1 + 2i)/(3 + 4i) x (1 - 2i)/(3 - 4i)

• Now we know the formula:

                  (a - b)(a + b) = a² - b²

• Applying this, we get:

                  (1² - (2i)²) / (3² - (4i)²)

                  1 - 4i² / 9 - 16i²

• Now we know that i² = -1, so:

                  1 - 4(-1) / 9 - 16(-1)

                  1 + 4 / 9 + 16

                  5/25 = 1/5

Answer:

                So the value of the given term is 1/5, yes it is a real number.