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:
a = 22
b = 31
c = 13
Step-by-step explanation:
The sum is the same in each row, column, and diagonal.
One of the diagonals is already complete. The sum is:
16 + 25 + 34 = 75
So the first row adds up to 75:
a + 37 + 16 = 75
a = 22
The second row adds up to 75:
19 + 25 + b = 75
b = 31
And the third row adds up to 75:
34 + c + 28 = 75
c = 13
We can check our answer by finding the sum of each column and the other diagonal.
22 + 19 + 34 = 75
37 + 25 + 13 = 75
16 + 31 + 28 = 75
22 + 25 + 28 = 75
Answer:
34.26
Step-by-step explanation:
514 divide by 15 cheesecakes is 34.26 repeating
Answer:
$5.60
Step-by-step explanation:
interest = 3.5% = 3.5 ÷ 100 = 0.035
So 3.5% of $400 = 0.035 x 400 = $14
If Jonah spend 3/5 of the interest, then he gives his brother 2/5 of the interest each year.
2/5 of $14 = 2/5 x 14 = $5.60
