SOLUTION: Let tan(A)=1/3 where {{{0<A<pi/2}}}
a) Show that 4A = {{{tan^-1(24/7)}}}
b) Given that {{{0<A<pi/2}}}, express z = 7 + 24i in the form {{{rcis(theta)}}} giving all the possible v
Question 1152857: Let tan(A)=1/3 where
a) Show that 4A =
b) Given that , express z = 7 + 24i in the form giving all the possible values of in terms of A.
c) Hence obtain in the form a + ib, the four fourth roots of z. Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website! .
I will answer part (a), ONLY.
Use the formula for tan(2A)
tan(2A) = = = = = .
Use the formula for tan(2A), again
tan(4A) = = = = = .
Therefore, 4A = .