Answer and step-by-step explanation:
The polar form of a complex number 
is the number 
where 
is called the modulus and 
is called the argument. You can switch back and forth between the two forms by either remembering the definitions or by graphing the number on Gauss plane. The advantage of using polar form is that when you multiply, divide or raise complex numbers in polar form you just multiply modules and add arguments.
(a) let's first calculate moduli and arguments
now we can write the two numbers as
(b) As noted above, the argument of the product is the sum of the arguments of the two numbers:
(c) Similarly, when raising a complex number to any power, you raise the modulus to that power, and then multiply the argument for that value.
![(z_1)^1^2=[4e^{-i\frac \pi6}]^1^2=4^1^2\cdot (e^{-i\frac \pi6})^1^2=2^2^4\cdot e^{-i(12)\frac\pi6}\\=2^2^4 e^{-i\cdot2\pi}=2^2^4](https://tex.z-dn.net/?f=%28z_1%29%5E1%5E2%3D%5B4e%5E%7B-i%5Cfrac%20%5Cpi6%7D%5D%5E1%5E2%3D4%5E1%5E2%5Ccdot%20%28e%5E%7B-i%5Cfrac%20%5Cpi6%7D%29%5E1%5E2%3D2%5E2%5E4%5Ccdot%20e%5E%7B-i%2812%29%5Cfrac%5Cpi6%7D%5C%5C%3D2%5E2%5E4%20e%5E%7B-i%5Ccdot2%5Cpi%7D%3D2%5E2%5E4)
Now, in the last step I've used the fact that 
, or in other words, the complex exponential is periodic with 
as a period, same as sine and cosine. You can further compute that power of two with the help of a calculator, it is around 16 million, or leave it as is.
Answer:
41000 meters
Step-by-step explanation:
multiply the length value by 1000
Answer:
4
Step-by-step explanation:
If you add up all of those, you get 24. Then you divide by 6. 24/6 = 4.
Answer:
For purple;
P(p) = 337/848 = 0.40
For white;
P(w) = 511/848 = 0.60
Step-by-step explanation:
Given;
Number of plants with purple flowers P = 337
Number of plants with white flowers W = 511
Total T = 337 + 511 = 848
For purple;
the empirical Probability that a plant had purple flowers P(p) is
P(p) = Number of plants with purple flowers/total number of plants
P(p) = P/T
Substituting the values, we have;
P(p) = 337/848 = 0.40
For white;
the empirical Probability that a plant had white flowers P(w) is
P(w) = Number of plants with white flowers/total number of plants
P(w) = W/T
Substituting the values, we have;
P(w) = 511/848 = 0.60
