If `cos(logi ^(4i) )=a+ib `, then find a and b.

If sin (log_(e)i^(i))=a+ib, where i=sqrt(-1), find a and b, hence and find cos(log_(e)i^(i)) .

If (2 + 3i)/(3 - 4i) = a + ib , find the values a and b.

If (1+ i sqrt(3))^(1999)=a+ib , then

If 1+1/i=A+iB , then find the value of B.

if cos (1-i) = a+ib, where a , b in R and i = sqrt(-1) , then

If tan A =a/b , then find the value of ("a sin A- b cos A")/("a sin A + b cos A") .

If (a+ib)= (1+i ) /(1-i) , then prove that (a ^2+b^ 2 )=1

(i) If 3A = 4B = 6C , find : A : B : C . (ii) If 2a = 3b and 4b = 5c , find: a : c .

If ((1+i)/(1-i))^3-((1-i)/(1+i))^3 =a+ib find a and b