Question

(3+2i)^60 solve by using demover theorem​

Answer 1

Answer:

The result of Equation 5.3.1 is not restricted to only squares of a complex number. If z=r(cos(θ)+isin(θ)), then it is also true that

z3=zz2=(r)(r2)(cos(θ+2θ)+isin(θ+2θ))=r3(cos(3θ)+isin(3θ))

We can continue this pattern to see that

z4=zz3=(r)(r3)(cos(θ+3θ)+isin(θ+3θ))=r4(cos(4θ)+isin(4θ))

The equations for z2, z3, and z4 establish a pattern that is true in general; this result is called de Moivre’s Theorem.