If `(x+i y)^5=p+i q ,` then prove that `(y+i x)^5=q+i pdot`

If x+iy=(2+i)/(2-i) then prove taht x^(2)+y^(2)=1

If (a+i b)^(5)=alpha+i beta then (b+i a)^(5)=

If ((1+i)/(1-i))^(x)=1 , then x=

If z=x-i y and z^(1 / 3)=p+i q then ((x)/(p)+(y)/(q)) div(p^(2)+q^(2))=

If x=ptantheta+ qsectheta and y=psectheta+qtantheta the prove that x^2-y^2=q^2-p^2 .

If sqrt(a+i b)=x+i y , then a possible value of sqrt(a-i b) is

If x+i y=(-1+i sqrt(3))^(2010) , then x=

If x^(p) . y^(q) = (x+y)^(p+q) , then dy/dx is equal to

If p, q, are real and p ne q then the roots of the equation (p-q) x^(2)+5(p+q) x-2(p-q)=0 are

A box contains n coins, Let P(E_(i)) be the probability that exactly i out of n coins are biased. If P(E_(i)) is directly proportional to i(i+1),1 leilen . Q. Proportionality constant k is equal to