What is an equation of the line that

Consider the complex number 𝑧 = −1 − 𝑖√2 

a) Using De Moivre’s Theorem, find 𝑧^3 𝑎𝑛𝑑 𝑧^5

b) Plot 𝑧, 𝑧^3 𝑎𝑛𝑑 𝑧^5 on an Argand Diagram.

Show directly from the definition that if ${\displaystyle \left(x_n\right)}$ and ${\displaystyle \left(y_n\right)}$ are Cauchy sequences, then ${\displaystyle (x_n+y_n)}$ and $\left(x_n{y}_n\right)$ are Cauchy sequences. 
If ${\displaystyle x_n=\sqrt{n}}$, show that ${\displaystyle \left(x_n\right)}$ satisfies ${\displaystyle lim\left|x_{n+1}–x_n\right|=0}$, but that it is not a Cauchy sequence. 
Let p be a given natural number and give an example of a sequence ${\displaystyle \left(x_n\right)}$ that is not a Cauchy sequence, but that satisfies ${\displaystyle lim\left|x_{n+p}–x_n\right|=0}$.

Estimate the terminal sped of a typical car having an engine with a constant power in a flat road, by using the concept of drag force.

An electric turntable 0.820 m in diameter is rotating about a fixed axis with an initial
angular velocity of 0.240 rev/s and a constant angular acceleration of 0.800 rev/s2
. 

(a)Compute the angular velocity of the turntable after 0.400 s. 

(b) Through how many
revolutions has the turntable spun in this time interval? 

(c) What is the tangential speed of
a point on the rim of the turntable at t= 0.400 s? 

(d) What is the magnitude of the
resultant acceleration of a point on the rim at t = 0.400 s?

Complete the square to transform the general equation below to standard form in order to determine the center and radius

Find the position vector of the point in space P that lies on the line AB such that with m,neR. Find the position vector of P if A(1,2,1), B(3,-1,2), m=3 and n =2.