Simplify: 3-4i/ 3+4i + 3+4i/ 3-4i

Mathematics

1 answer:

Greeley [361]4 years ago

5 0

Answer:

-14/25

Step-by-step explanation:

Remember i^2 = -1. Otherwise, the math is the same as for any polynomials.

$\dfrac{3-4i}{3+4i}+\dfrac{3+4i}{3-4i}=\dfrac{(3-4i)(3-4i)+(3+4i)(3+4i)}{(3+4i)(3-4i)}\\\\=\dfrac{(9-24i-16)+(9+24i-16)}{9+16}=\boxed{-\dfrac{14}{25}}$

You might be interested in

A ladder is leaning up against a house. The ladder is 20 feet long and the base of the ladder is 12 feet away from the house. Ho

MrRa [10]

Answer:

16 feet

Step-by-step explanation:

The length of the ladder=20 feet

Distance from the base of the ladder to the house = 12 feet

You will notice that a wall is vertical and the ladder makes an angle with the horizontal ground(making it the hypotenuse). This is a right triangle problem.

To find the how far up the house can the ladder can reach, we simply find the third side of the right triangle.

From Pythagoras theorem

$Hyp^2=Opp^2+Adj^2\\20^2=12^2+Adj^2\\Adj^2=400-144\\Adj^2=256\\Adj=\sqrt{256}=16$