Prove that `t a n(i(log)_e((a-i b)/(a+i b)))=(2a b)/(a^2-b^2)(w h e r ea ,b in R^+)`

tan [i log ((a-i b)/(a+i b))]=

The value of (a+i b)^(m / n)+(a-i b)^(m / n) is equal to

Determine which of the following binary opertions on the set R are associative and which are commutative. (a) a **b =1 AA a, b in R (b) a **b = ((a +b))/( 2) AA a,b in R

Prove that 2^(sqrt((log)_a4sqrt(a b)+(log)_b4sqrt(a b))-(log)_a4sqrt(b/a)+(log)_b4sqrt(a/b))dotsqrt((log)_a b)={2ifbgeqa >1 and 2^(log_a(b) if 1 < b < a

Let R be a relation from Q to Q defined by R={(a,b): a,b in Q and a-b in Z} . Show that (i) (a,a) in R" for all " a in Q (ii) (a,b) in R implies that (b,a) inR (iii) (a,b) in R and (b,c) in R implies that (a,c) in R

If z=x+i y, z^(1 / 3)=a-i b and (x)/(a)-(y)/(b)=k(a^(2)-b^(2)) then the value of k=

Prove log_(b)b = 1

Given a^2+b^2=c^2 . Prove that log_(b+c)a+log_(c-b)a=2 log_(c+b)a.log_(c-b)a,forallagt0,ane1 c-bgt0 , c+bgt0 c-bne1 , c+bne1 .

If x+i y=sqrt((a+i b)/(c+i d)) then (x^(2)+y^(2))^(2)=

The value of a^((log_b(log_b N))/(log_b a)), is