x (3-5) + (4b)
= x ( -2) + (4b), since x=8 b=3
= -16 + 12
= -4
What I did there is substitution
Replacing x with 8 ,and b with 3
So -16 is the product of (-2) and 8
And 12 is the product of 4 and 3
FYI: -2 is the result of 3 - 5
Answer:
No.
Step-by-step explanation:
you don't give out any personal info for us to take therefore we have nothing to steal
Answer:
![\bold{4\sqrt3 + i4}](https://tex.z-dn.net/?f=%5Cbold%7B4%5Csqrt3%20%2B%20i4%7D)
Step-by-step explanation:
Given complex number is:
![[2(cos10^\circ + i sin10^\circ)]^3](https://tex.z-dn.net/?f=%5B2%28cos10%5E%5Ccirc%20%2B%20i%20sin10%5E%5Ccirc%29%5D%5E3)
To find:
Answer in rectangular form after using De Moivre's theorem = ?
i.e. the form
(not in forms of angles)
Solution:
De Moivre's theorem provides us a way of solving the powers of complex numbers written in polar form.
As per De Moivre's theorem:
![(cos\theta+isin\theta)^n = cos(n\theta)+i(sin(n\theta))](https://tex.z-dn.net/?f=%28cos%5Ctheta%2Bisin%5Ctheta%29%5En%20%3D%20cos%28n%5Ctheta%29%2Bi%28sin%28n%5Ctheta%29%29)
So, the given complex number can be written as:
![[2(cos10^\circ + i sin10^\circ)]^3\\\Rightarrow 2^3 \times (cos10^\circ + i sin10^\circ)^3](https://tex.z-dn.net/?f=%5B2%28cos10%5E%5Ccirc%20%2B%20i%20sin10%5E%5Ccirc%29%5D%5E3%5C%5C%5CRightarrow%202%5E3%20%5Ctimes%20%28cos10%5E%5Ccirc%20%2B%20i%20sin10%5E%5Ccirc%29%5E3)
Now, using De Moivre's theorem:
![\Rightarrow 2^3 \times (cos10^\circ + i sin10^\circ)^3\\\Rightarrow 8 \times [cos(3 \times10)^\circ + i sin(3 \times10^\circ)]\\\Rightarrow 8 \times (cos30^\circ + i sin30^\circ)\\\Rightarrow 8 \times (\dfrac{\sqrt3}2 + i \dfrac{1}{2})\\\Rightarrow \dfrac{\sqrt3}2\times 8 + i \dfrac{1}{2}\times 8\\\Rightarrow \bold{4\sqrt3 + i4}](https://tex.z-dn.net/?f=%5CRightarrow%202%5E3%20%5Ctimes%20%28cos10%5E%5Ccirc%20%2B%20i%20sin10%5E%5Ccirc%29%5E3%5C%5C%5CRightarrow%208%20%5Ctimes%20%5Bcos%283%20%5Ctimes10%29%5E%5Ccirc%20%2B%20i%20sin%283%20%5Ctimes10%5E%5Ccirc%29%5D%5C%5C%5CRightarrow%208%20%5Ctimes%20%28cos30%5E%5Ccirc%20%2B%20i%20sin30%5E%5Ccirc%29%5C%5C%5CRightarrow%208%20%5Ctimes%20%28%5Cdfrac%7B%5Csqrt3%7D2%20%2B%20i%20%5Cdfrac%7B1%7D%7B2%7D%29%5C%5C%5CRightarrow%20%5Cdfrac%7B%5Csqrt3%7D2%5Ctimes%208%20%2B%20i%20%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%208%5C%5C%5CRightarrow%20%5Cbold%7B4%5Csqrt3%20%2B%20i4%7D)
So, the answer in rectangular form is:
![\bold{4\sqrt3 + i4}](https://tex.z-dn.net/?f=%5Cbold%7B4%5Csqrt3%20%2B%20i4%7D)
Answer:
slope = (x1-x2)/(y1-y2)
so take any 2 points , for example:
(0,1) and (2,2) (order doesn't matter)
(0-2)/(1-2) = -2/-1 = 2 (gradient/slope)