CPhill

The percent increase is given by

(New Value - Old Value)/ Old Value

The pecent decrease is given by

(Old Value - New Value)/Old Value

For instance, if something increased from 8 to 10, the  percent increase is just

(10 - 8)/ 8 = 2/8 = 1/4 = 25%

But, if something went from 10 to 8, the percent decrease is just

(10 - 8) / 10 = 2/10 = 20%

Sin(5pi/6) is just a 30 degree angle in the second quadrant.....and the sine of 30 degrees is 1/2

1. z1 = 1-i and z2 = 3i   z1/z2 = ?

( 1 -i) / (3i)   * (3i) / (3i) =

(1 -i) (3i)  / 9i^2  =

(1 -i)(3i) / -9 =

( i -1)(3i) / 9 =

3i^2/ 9 -  3i/9  =

-3/9 - i/3 =

-1/3 - i/3

2. z1 = 1+2i and z2 = 1+i  z1/z2 = ?

(1 + 2i) / (1 + i)   *   (1 -i) / (1 - i)  =

(1 + 2i)(1- i) / (1 - i^2) =

(1 + 2i)(1- i) / (1 - -1) =

(1 + i -2i^2) / 2  =

(1 + i + 2) / 2 =

(3 + i) /2=

3/2 + i/2

tan(5pi/6) = -1 /√3 = -√3 / 3

15% off 30 is the same as 85% of 30....!!!

Good !!!

So we have

√(3 +√5) - √(3 -√5)

Let   √(3 +√5) - √(3 -√5)  =  x   = √(x^2)

So we have

√ [√(3 +√5) - √(3 -√5)]^2 =

√ [3 + √5 - 2√(3 +√5)√(3 -√5)+ 3 -√5 ] =

√ [3 - 2√(9-5) + 3] =

√ [6 -2√4] =

√ [6 - 2*2] =

√(6-4) =

√2

P.S.   -  That was a neat little trick I learned from another member......heureka .....!!!

Thanks, heureka !!!

I mean that 0 + 0 is easier....!!!

I just thought it was a typo, Tiddle.....!!!!

Ah...you got me there !!!