Solve the quartic equation, w^4+(5+10i)w^2-48+14i=0 by realizing the following plan. (i) Find the solutions z1, z2 of the auxiliary quadratic equation z^2+(5+10i)z-48+14i=0
Solve the quartic equation,
w^4+(5+10i)w^2-48+14i=0 by realizing the following plan.
(i) Find the solutions z1, z2 of the auxiliary
z^2+(5+10i)z-48+14i=0
Here, and in the next part (ii), any extraction of the roots of degree two of a complex u ∈ C must be done with the use of a scientific calculator; to show your work, please make sure to provide
(a) the code for a scientific calculator you have used and (b) approximations of the module r = |u| and the argument θ = arg(u) of u to five decimal places.
(ii) Find the roots w1, w2 of degree two of z1 and then the roots w3, w4 of degree two of z2, thereby obtaining all four solutions of the original equation.
Please give a complete solution to the problem.
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