Math Problems

Critical Thinking Math Problems: Examples and Activities

SOLVED:Consider the following problems related to computation with complex numbers. (a) Find and plot all roots of (i) z^3=-1, (ii) z^2=1 (iii) z^2+3 z+1=0 (b) Suppose you want to find the natural logof a complex number z=|z| e^j θ, which is log(z)=log(|z| e^j θ)=log(|z|)+log(e^j θ)=log(|z|)+j θIf z is negative it can be written as z=|z| e^e x and we can find log(z) by using the above derivation. The natural log of any complex number can be obtained this way also. Justify each one of the steps i