Home
Class 11
MATHS
If x+iy = (a+ib)/(a-ib), prove that x^(2...

If `x+iy = (a+ib)/(a-ib)`, prove that `x^(2) + y^(2)=1`.

Text Solution

Verified by Experts

The correct Answer is:
1
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NCERT BANGLISH|Exercise EXERCISE 5.1|14 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NCERT BANGLISH|Exercise EXERCISE 5.2|8 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NCERT BANGLISH|Exercise MISCELLANEOUS EXERCISES ON CHAPTER 24|1 Videos

  • BINOMIAL THEOREM

    NCERT BANGLISH|Exercise Miscellanous exercise on chapter 8|10 Videos

  • CONIC SECTIONS

    NCERT BANGLISH|Exercise Miscellaneous Exercise|8 Videos

Similar Questions

Explore conceptually related problems

If x-iy = sqrt((a+ib)/(c-id)) , prove that (x^(2) + y^(2))^(2) = (a^(2) + b^(2))/(c^(2) + d^(2))

If x+iy=sqrt((a+ib)/(c+id))" ""prove that", (x^(2)+y^(2))^(2)=(a^(2)+b^(2))/(c^(2)+d^(2))

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

If z=x+iy and |2z-1|=|z-2|," prove that" " " x^(2)+y^(2)=1.

If z=x+iy and |z+6|=|2z+3|, porve that x^(2)+y^(2)=9.

If y= 2^((1)/(log_(x)4)) then prove that x=y^(2) .

If y=x log((1)/(ax)+(1)/(a)) , prove that, x(x+1)y_(2)+xy_(1)=y-1 .

If y=((1+x)/(1-x))^(n) , prove that (1-x^(2))(d^(2)y)/(dx^(2))=2(n+x)(dy)/(dx).

If (a+ib)/(c+id)=x+iy prove that, (a^(2)+b^(2))/(c^(2)+d^(2))=x^(2)+y^(2)

If x+iy=((a+ib)/(c+id))^(1//2) ,show that (x^2+y^2)=(a^2+b^2)/(c^2+d^2)