Answers:
<u>Reduce:</u>
Here we gave to simplify the expressions:
9) 
Grouping similar terms:

Applying common factor
in the first parenthesis and common factor
in the second parenthesis:
This is the answer
11) 
Rearranging the terms:

Applying common factor
in the first parenthesis and common factor
in the second parenthesis:
This is the answer
<u>Multiply:</u>
19) 
Multiplying both fractions:

Dividing numerator and denominator by 3 and simplifying:
This is the answer
21) 

Operating with cross product:


Grouping similar terms and factoring:
This is the answer
<u>Divide:</u>
29) 

Simplifying:
This is the answer
33) 

Factoring numerator and denominator:

Simplifying:
This is the answer
37) 

Applying the distributive property in numerator and denominator:

Grouping similar terms and factoring by common factor:

Dividing by
in numerator and denominator and simplifying:
This is the answer
We need some sort of diagram to see what they are. Is there any way to say that ac = db? Either equal angles or equal lines.
x + 3 = 3x - 19 Add 19
x + 3 + 19 = 3x Subtract x
21 = 2x
x = 21 / 2
x = 10.5
ac = 10.5 + 3
x = 13.5
Answer:
(C) because the answer is 69
Step-by-step explanation:
you make 3 groups of 23 and u get 69
its greater then 23 and 4
and its not between 3 and 4 or between 23 or 3
so it can only be (C)
By using <span>De Moivre's theorem:
</span>
If we have the complex number ⇒ z = a ( cos θ + i sin θ)
∴
![\sqrt[n]{z} = \sqrt[n]{a} \ (cos \ \frac{\theta + 360K}{n} + i \ sin \ \frac{\theta +360k}{n} )](https://tex.z-dn.net/?f=%20%5Csqrt%5Bn%5D%7Bz%7D%20%3D%20%20%5Csqrt%5Bn%5D%7Ba%7D%20%5C%20%28cos%20%5C%20%20%5Cfrac%7B%5Ctheta%20%2B%20360K%7D%7Bn%7D%20%2B%20i%20%5C%20sin%20%5C%20%5Cfrac%7B%5Ctheta%20%2B360k%7D%7Bn%7D%20%29)
k= 0, 1 , 2, ..... , (n-1)
For The given complex number <span>⇒ z = 81(cos(3π/8) + i sin(3π/8))
</span>
Part (A) <span>
find the modulus for all of the fourth roots </span>
<span>∴ The modulus of the given complex number = l z l = 81
</span>
∴ The modulus of the fourth root =
Part (b) find the angle for each of the four roots
The angle of the given complex number =

There is four roots and the angle between each root =

The angle of the first root =

The angle of the second root =

The angle of the third root =

The angle of the fourth root =
Part (C): find all of the fourth roots of this
The first root =

The second root =

The third root =

The fourth root =