Home
Class 12
MATHS
If (p+iq)/(r+is) = x + iy , prove tha...

If ` (p+iq)/(r+is) = x + iy ` , prove that `(p-iq)/(r-is) = x -iy and (p^(2)+q^(2))/(r^(2)+s^(2))=x^(2)+y^(2)` ,where `p,q,r,s,x,y,inR`

Text Solution

AI Generated Solution

To prove the given statements, we start with the equation: \[ \frac{p + iq}{r + is} = x + iy \] ### Step 1: Taking the Conjugate We take the conjugate of both sides of the equation. The conjugate of a complex number \( z = a + ib \) is \( \overline{z} = a - ib \). Thus, we have: ...
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Try Yourself|60 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section -A) (objective Type Questions ( one option is correct)|47 Videos

  • BINOMIAL THEOREM

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (section-J) Objective type question (Aakash Challengers Questions)|4 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J ( Aakash Challengers Questions )|16 Videos

Similar Questions

Explore conceptually related problems

if p: q :: r , prove that p : r = p^(2): q^(2) .

If P + Q = R and P - Q = S, prove that R^2 + S^2 = 2(P^2 + Q^2)

If a=x y^(p-1),\ b=x y^(q-1) and c=x y^(r-1) , prove that a^(q-r)b^(r-p)\ c^(p-q)=1

if q is the mean proportional between p and r , prove that : p^(2) - q^(2) + r^(2) = q^(4) ((1)/(p^(2))-(1)/(q^(2)) + (1)/(r^(2))) .

If p, q, r are rational then show that x^(2)-2px+p^(2)-q^(2)+2qr-r^(2)=0

In Figure, /_P Q R=\ /_P R Q , then prove that /_P Q S=\ /_P R Tdot

In Fig. 6.15, /_P Q R=/_P R Q , then prove that /_P Q S=/_P R T .

If z = x - iy and z'^(1/3) = p +iq, then 1/(p^2+q^2)(x/p+y/q) is equal to

If z = x - iy and z'^(1/3) = p +iq, then 1/(p^2+q^2)(x/p+y/q) is equal to

For p, q in R , the roots of (p^(2) + 2)x^(2) + 2x(p +q) - 2 = 0 are