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Find the conjugates of the following com...

Find the conjugates of the following complex number: `1/(3+5i)`

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To find the conjugate of the complex number \( \frac{1}{3 + 5i} \), we will follow these steps: ### Step 1: Identify the Complex Number The complex number we are working with is \( z = 3 + 5i \). ### Step 2: Find the Conjugate of the Complex Number The conjugate of a complex number \( a + bi \) is given by \( a - bi \). Therefore, the conjugate of \( 3 + 5i \) is: \[ ...
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RD SHARMA-COMPLEX NUMBERS-Solved Examples And Exercises
  1. Find the real values of x\ a n d\ y ,\ if:(1+i)(x+i y)=2-5i

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  2. Find the conjugates of the following complex number: 4-5i

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  3. Find the conjugates of the following complex number: 1/(3+5i)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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