Which expressions are equal to a real number?

Option B

Option C

Step-by-step explanation:

⇒ , which is a real number.

Similarly,

And we also know that

So, we see that odd powers of is a complex number and even powers renders us a real number.

Using this we solve the problem.

Option A: 11 is an odd power. This would be a complex number and not a real number.

Option B: Even power of i. So, this should give us a real number.

Option C:

                            (a + bi)² = a² - b² + 2abi

So, (2 + 3i)² would be a complex number because of the 2bi term.

Option D: (4 + 5i)(4 - 5i)

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

So, (4 + 5i)(4 - 5i) = 4² + 5² = 41, a real number.

Option E: (6 + 8i)(8 + 6i)

                     (a + ib)(c + id) = ac - bd + (ad + bc)i

This would be a complex number because of the (ad + bc) term.

So, Options B and D are real numbers.

a rotation about point l

step-by-step explanation:

quizlet

answer is 33

step-by-step explanation: