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Prove that Re (z1 z2)= Re z1 Re z2 - Imz...

Prove that `Re (z_1 z_2)= Re z_1 Re z_2 - Imz_1 Imz_2` ,

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MODERN PUBLICATION-COMPLEX NUMBERS-MISCELLANEOUS EXERCISE ON CHAPTER
  1. Evaluate : [i^(18)+(1/i)^(25)]^3

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  2. Prove that Re (z1 z2)= Re z1 Re z2 - Imz1 Imz2 ,

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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 - i y =sqrt((a-i b)/(c-i d))prove that x^2+y^2=(a^2+b^2)/(c^2+d^2...

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

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

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  7. Solve the equation :x^2-2x+3/2=0

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  8. Solve the equation :27 x^2-10 x+1=0

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  9. Solve the equation :21 x^2-28 x+10=0

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  10. If z1=2-i ,\ z2=1+i , find |(z1+z2+1)/(z1-z2+i)|

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

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  12. Let z1=2-i ,z2=-2+i. Find (i) Re ((z1z2)/( bar z1)) (ii) Im(1/(z1 bar...

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

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  14. Find the real numbers x\ a n d\ y , if (x-i y)(3+5i) is the conjugate ...

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

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

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  17. If alphaand betaare different complex numbers with |beta|=1,then fin...

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  18. Find the number of non-zero integral solution of the equation |1-i|^x=...

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  19. If (a + i b) (c + i d) (e + if) (g + i h) = A + i B, then show that (a...

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  20. If ((1+i)/(1-i))^m=1, then find the least integral value of m

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