confidence interval

confidence interval for population proportion (P) is

( p - (z)sqrt(pq/n) , p + (z)sqrt(pq/n) )

where z is the table value corresponding to the required confidence level, (two tailed)
p the sample proportion , q = 1 - p
n = sample size

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inverse and direct variation

u is said to be directly proportional to v if u = c v for some constant c

u is said to be inversely proportional to v if u = [k / v] for some constant k

In direct variation, u increases as v increases and vice versa.

In inverse variation, u decreases as v increases and vice versa.


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problem of splitting into real and imaginary parts

if u+iv = (x +iy) ^3 , show that (u/x) + (v/y) = 4( x² -y² )

first expand (x +iy) ^3 using binomial expansion or identity and then split into real and imaginary parts then manipulate


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