SOLUTION: Q.1 If {{{ (x+iy)^(1/3)=a+ib }}} then show that {{{ 4(a^2 - b^2)=x/a + y/b }}} Q.2 Find the real no.s x and y if {{{ (x-iy)(3+5i) }}} is the conjugate of {{{ -6-24i }}} .

Question 1060987: Q.1 If then show that
Q.2 Find the real no.s x and y if is the conjugate of .
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Q.1 <--->

---> --->
So,

Q.2
The conjugate of is .
--> -->
There are many ways to solve the system. For example,
we could start by multiplying the first equation times ( , the second equation times and adding them to get
--> --> --> .
Then, substituting for in , we get
--> --> --> --> --> .
RELATED QUESTIONS
If x+iy=(a+ib)*(a+ib)*(a+ib) then show that x/a+y/b=4(a^2-b^2) PLZ... (answered by J2R2R)

Given that √(x + iy) = a + ib, so that x = a^2 + b^2, y = 2ab and find a and b if x (answered by ikleyn)

solve the following equation for real numbers x and y.... (answered by ikleyn)

if (x+iy)^3=y+vi then show that... (answered by josgarithmetic)

Express (x + iy)(u - iv)(x - iy)(u + iv) in the form a + ib, where a, b €... (answered by MathLover1)

If z = {{{(x+i(y+2))/((x+1)+iy)}}}, w = x+iy and |z| = 2, Find the locus of w.... (answered by ikleyn)

(x-iy)(x+iy), where x and y are real numbers. Give your final answer in the form... (answered by josgarithmetic)

solve the following equation for real numbers x and y. ((1+i)/(1-i))^2+1/(x+iy)=1+i. (answered by Alan3354)

if z=x+iy , z* conj(z)^3+conj(z)*z^3=350, then (x,y)=..[(2,1) ,(3,4) ,(4,3)... (answered by ikleyn)