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For any two complex numbers z(1) and z(2...

For any two complex numbers `z_(1)` and `z_(2)`, prove that Re (`z_(1)z_(2)) = Re z_(1) Re z_(2)- 1mz_(1) Imz_(2)`

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The correct Answer is:
`Re(z_(1))Re(z_(2))-Im(z_(1))Im(z_(2))`
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KUMAR PRAKASHAN-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-MISCELLANEOUS EXERCISE :
  1. Evaluate [i^(18) + (1/i)^(25)]^(3)

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  2. For any two complex numbers z(1) and z(2), prove that Re (z(1)z(2)) = ...

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  3. Reduce (1/(1-4i) -2/(1+i))((3-4i)/(5+i)) to the standard form.

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

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  5. Conver the following in the polar form: (i) (1+7i)/(2-i)^(2), (ii) (...

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  6. Conver the following in the polar form: (i) (1+7i)/(2-i)^(2), (ii) (...

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  7. Solve: 3x^(2) - 4x + 20/3=0

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  8. x^(2)-2x + 3/2=0

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  9. 27x^(2) - 10x +1=0

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  10. 21x^(2) - 28x + 10=0

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  11. If z^(1) =2 -I, z(2)=1+i, find |(z(1) + z(2) + 1)/(z(1)-z(2) + 1)|

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

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  13. Let z(1) =2-I, z(2) =-2 + i, Find (i) (Re(z(1)z(2))/barz(1)), (ii) I...

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  14. Find the modulus and argument of the complex number (1+2i)/(1-3i)

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  15. Find the real numbers x and y if (x-iy) (3+5i) is the conjugate of -6 ...

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  16. Find the modulus of (1+i)/(1-i) - (1-i)/(1+i)

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

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  18. If alpha and beta are different complex numbers with |beta|=1, then fi...

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  19. Find the numbers of non-zero integral solutions of the equation |1-i|^...

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  20. If (a+ib)(c+id)(e+if)(g+ih) = A + iB, then show that (a^(2) + b^(2))...

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