hectictar

avatar
Usernamehectictar
Score9460
Membership
Stats
Questions 10
Answers 3005

 #3
avatar+9460 
+3

This video really helped me understand: https://www.youtube.com/watch?v=BZxZ_eEuJBM

 

 

If     \(z=-8+15i\)     then     \(\overline{z}=-8-15i\)

 

If     \(w=6-8i\)     then     \(\overline{w}=6+8i\)

 

 

And so...

 

 

\(\dfrac{z\overline{z}}{w\overline{w}}\ =\ \dfrac{(-8+15i)(-8-15i)}{(6-8i)(6+8i)}\ =\ \dfrac{(-8)^2-(15i)^2}{(6)^2-(8i)^2}\ =\ \dfrac{64+225}{36+64}\ =\ \dfrac{289}{100}\)

 

 

Just like CPhill found. laugh

Jun 24, 2019
 #1
avatar+9460 
+3

Using the short scale definitions from the table here: https://en.wikipedia.org/wiki/Names_of_large_numbers

 

 

72.1 Quadrillion=72.1 × 1015=72.1 × 1015=7.21 × 1016=72 100 000 000 000 000
 ___ ___ ___ ___ 
1000 Trillion × 72=103 × 1012 × 72=72 × 1015=7.2 × 1016=72 000 000 000 000 000

 

 

So  72.1 Quadrillion  is pretty close to  100 Trillion × 72  but they're not exactly the same.

 

( If you use the long scale definitions you get  72.1 × 1024  and  72 × 1021   which are further apart.)

 

 

And neither are equal to  1072  .   1072  is  1  with  72  zeros after it.

 

1072  =  1 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000

Jun 22, 2019
 #1
avatar+9460 
+3

I found three different possible values of  d  using this graph:

 

https://www.desmos.com/calculator/cwbrobjoav

 

You can turn on the different parallelograms by clicking the circle next to the name.

Here's a picture with all of them turned on:

 

The different possible values of  d  are:

 

 

-3 + 6i

 

5 - 10i

 

 

11 + 0i  
Jun 20, 2019