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Find the modulus and argument of the fol...

Find the modulus and argument of the following complex number and hence express them in the polar form: `\ sqrt(3)+i`

Text Solution

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let `z=sqrt3+i`
then, ` |z|=sqrt((sqrt3)^2+(1))=2`
let `theta` be the argument of z and `alpha` be the acute angle given by `tan theta =(|im(z))/(re(z)|`
`tan alpha = 1/sqrt3`
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RD SHARMA-COMPLEX NUMBERS-Solved Examples And Exercises
  1. Find the modulus and argument of the following complex number and henc...

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  2. Find the modulus and argument of the following complex number and henc...

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  3. Find the modulus and argument of the following complex number and henc...

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  4. Find the modulus and argument of the following complex number and henc...

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  5. Find the modulus and argument of the following complex number and henc...

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  6. Find the modulus and argument of the following complex number and henc...

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  7. Write (i^(25))^3 in polar form.

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  8. Write the values of the square root of idot

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  9. Write the values of the square root of -i.

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  10. If x+i y=sqrt((a+i b)/(c+i d)), then write the value of (x^2+y^2)^2.

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  11. If pi<theta<2pi\ a n d\ z=1+costheta+isintheta , then write the value ...

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  12. If n is any positive integer, write the value of (i^(4n+1)-i^(4n-1))/2...

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  13. Write the value of (i^(592)+i^(590)+i^(588)+i^(586)+i^(584))/(i^(582)+...

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  14. Write 1-i in polar form.

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  15. Write -1+isqrt(3)\ in polar form.

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  16. Write the argument of idot

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  17. Find the principal argument of (1+isqrt(3))^2dot

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  18. Find z ,\ if\ |z|=4\ and \ arg(z)=(5pi)/6 .

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  19. Write the value of sqrt(-25)xxsqrt(-9)dot

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  20. Write the value of a r g(z)+a r g( z ) .

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