◆ COMPLEX NUMBERS ◆
125 ( cos 288 + i sin 288 ) can be written as -
125.e^i( 288)
125.e^i( 288 +360 )
125.e^i( 288+ 720)
[ As , multiples of 360 can be added to an angle without changing any trigonometric functions or sign ]
To find the cube root , take the cube root of above 3 expressions ,
We get -
5 e^( i 96 )
5 e^( i 216 )
5 e^( i 336 )
Now using Euler's formula , We rewrite above as -
5 ( cos 96 + i sin 96 )
5(c os 216 + i sin 216 )
5 ( cos 336 + i sin 336 ) Ans.
we can always find the slope of any line by simply using two points on the line, say let's use (3,4) and (-1,2)
To calculate expected value,
We can add up the probability of all possible events.
The 2 possible events are either winning $50 or losing the prize, which is $ - 50
Expected value =
50 x 40 % + (-50) x 60%
= $-10
So the answer is $-10
