Let the given complex number
z = x + ix = 
We have to find the standard form of complex number.
Solution:
∴ x + iy =
Rationalising numerator part of complex number, we get
x + iy = 
⇒ x + iy = 
Using the algebraic identity:
(a + b)(a - b) = 
- 
⇒ x + iy = 
⇒ x + iy = 
[ ∵ 
]
⇒ x + iy = 
⇒ x + iy = 
⇒ x + iy = 
⇒ x + iy = 1 - i
Thus, the given complex number in standard form as "1 - i".
<span>2.607 x 10^13 dollars per person.
Avogadro's number is approximately 6.0221409x10^23.
So divide by the 231 million people. Giving
(6.0221409 x 10^23) / (231 x 10^6) = 0.02607 x 10^17
= 2.607 x 10^15 pennies
But we want dollars, so divide by 100
2.607 x 10^15 / 100 = 2.607 x 10^13 dollars</span>
The three numbers are 12, 18 and 24
Arithmetic progression
Let the 3 number in arithmetic progression be:
a-d, d, a+d ...
If their sum is 3, then;
a-d+d+a+d = 3
2a + d = 3 ........... 1
If the sum of their squares is 11, then;
(a-d)² + d² + (a+d)² = 11
a²-2ad+d²+d²+a²+2ad+d² 11
2a²+3d² = 11 ....... 2
Solving the equations simultaneously, d = 6 and a = 12
First-term = 12
second term = 18
Thirs term = 24
Hence the three numbers are 12, 18 and 24
Hope this helps you!!!!!! :D
3√24= 3√2^2*6 = 3*2√6 = 6√6
2√384= 2√8^2*6 = 2*8√6 = 16√6
√96= √4^2*6 = 4√6
6√6 -16√6- 4√6 = -14√6
Final answer: -14√6
