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

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

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To prove that \((y + i x)^5 = q + i p\) given that \((x + i y)^5 = p + i q\), we can follow these steps: ### Step 1: Start with the given equation We have: \[ (x + i y)^5 = p + i q \] ...
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CENGAGE ENGLISH-COMPLEX NUMBERS-ILLUSTRATION
  1. If the imaginary part of (2z+1)//(i z+1) is -2, then find the locus of...

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  2. If z is a complex number such that |z - barz| +|z + barz| = 4 then fi...

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

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  4. If z = x + iy lies in the third quadrant, then prove that (barz)/(z) ...

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  5. Let z = ((sqrt(3))/(2) + (i)/(2))^(5)+((sqrt(3))/(2)-(i)/(2))^(5). If ...

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  6. Find the relation if z1, z2, z3, z4 are the affixes of the vertices of...

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  7. Let z1, z2, z3 be three complex numbers and a ,b ,c be real numbers no...

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  8. Find real values of x and y for which the complex numbers -3+i x^2y an...

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  9. about to only mathematics

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  10. If (x+i y)^3=u+i v ,then show that u/x+v/y=4(x^2-y^2).

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  11. Let z be a complex number satisfying the equation z^2-(3+i)z+m+2i=0,w ...

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  12. Show that the equation Z^4+2Z^3+3Z^2+4Z+5=0 has no root which is eithe...

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  13. Find the square root of the following: 5+12 i

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  14. Find all possible values of sqrt(i)+sqrt(-i)dot.

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  15. Solve for z : z^2-(3-2i)z=(5i-5)dot

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  16. Solve the equation (x-1)^3+8=0 in the set C of all complex numbers.

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  17. If n is n odd integer that is greater than or equal to 3 but not a mul...

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  18. omega is an imaginary root of unity. Prove that If a+b+c = 0 th...

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  19. Find the complex number omega satisfying the equation z^3=8i and lying...

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  20. (1)/(a + omega) + (1)/(b+omega) +(1)/(c + omega) + (1)/(d + omega) =(1...

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