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Find the conjugates of the following com...

Find the conjugates of the following complex number: `((3-i)^2)/(2+i)`

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To find the conjugate of the complex number \(\frac{(3-i)^2}{2+i}\), we will first simplify the expression and then determine its conjugate. ### Step 1: Simplify the numerator \((3-i)^2\) Using the formula for the square of a binomial, we have: \[ (3-i)^2 = 3^2 - 2 \cdot 3 \cdot i + i^2 = 9 - 6i + (-1) = 8 - 6i \] ...
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RD SHARMA-COMPLEX NUMBERS-Solved Examples And Exercises
  1. Find the conjugates of the following complex number: 1/(1+i)

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  2. Find the conjugates of the following complex number: ((1+i)(2+i))/(3+i...

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  3. Find the conjugates of the following complex number: ((3-i)^2)/(2+i)

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  4. Find the conjugates of the following complex number: ((3-2i)(2+3i))/((...

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  5. Find the multiplicative of the following complex number: 1-i

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  6. Find the multiplicative of the following complex number: \ 4-3i

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  7. Find the multiplicative of the following complex number: (1+isqrt(3))^...

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  8. Find the multiplicative of the following complex number: sqrt(5)+3i

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

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  10. If z1=2-i ,\ z2=-2+i , find : R e((z1z2)/bar(z1))

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  11. If z1=2-i ,\ z2=-2+i , find : Im(1/(z1bar(z1))).

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

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  13. If x+i y=(a+i b)/(a-i b) prove that x^2+y^2=1

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  14. Write the least positive integral value of n for which ((1+i)/(1-i))^n...

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  15. Find the real values of theta for which the complex number (1+i costhe...

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  16. Find the smallest positive integer value of n for which ((1+i)^n)/((1-...

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  17. If ((1+i)/(1-i))^3-((1-i)/(1+i))^3=x+i y ,\ find\ (x , y)

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  18. If ((1-i)/(1+i))^(100)=a+i b , find(a , b)

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  19. Evaluate the following: 2x^3+2x^2-7x+72 ,\ w h e n\ x=(3-5i)/2

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  20. Evaluate x^4-4x^3 + 4x^2 + 8x + 44, when x = 3 + 2i

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