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Find the multiplicative of the following...

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

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Given `sqrt(5)+3i`
And we have to find multiplicative inverse of this.
Let `z=x+iy` be multiplication inverse of `sqrt(5)+3i`
then we have
`(x+iy)(sqrt(5)+3i)=1`
`sqrt(5)x+3ix+isqrt(5)y+3y(i^2)=1`
Since `(i^2)=-1`
`sqrt(5)x+3ix+isqrt(5)y-3y=1`
...
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RD SHARMA-COMPLEX NUMBERS-Solved Examples And Exercises
  1. Find the multiplicative of the following complex number: \ 4-3i

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Evaluate the following:\ x^4+4x^3+6x^2+4x+9,\ w h e n\ x=-1+isqrt(2)

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  17. Evaluate the following: x^6+x^4+x^2+1,\ w h e n\ x=(1+i)/(sqrt(2))

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  18. Evaluate the following: \ 2x^4+5x^3+7x^2-x+41 ,\ w h e n\ x=-2-sqrt(3)...

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  19. If z1 is a complex number other than -1 such that |z1|=1\ a n d\ z2=(z...

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  20. Solve the system of equations R e(z^2)=0,\ |z|=2

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