Calculate the product of the complex numbers below.

Question

(3-4i)(3+4i)

Answer 1

To calculate the product of complex numbers, we can use the formula (a + bi)(c + di) = (ac - bd) + (ad + bc)i.

In this case, a = 3, b = -4i, c = 3, and d = 4i.

Plugging in these values:

(3 - 4i)(3 + 4i) = (3 * 3) + (3 * 4i) + (-4i * 3) + (-4i * 4i)

Simplifying further:

= 9 + 12i - 12i - 16i^2

Since i^2 = -1, we can substitute that in:

= 9 + 12i - 12i - 16(-1)

= 9 + 12i - 12i + 16

Combining like terms:

= 25

Therefore, (3 - 4i)(3 + 4i) = 25.