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Express each of the following in the for...

Express each of the following in the form `a+i b :(-2-1/3i)^3`

Text Solution

Verified by Experts

GIven that,
`(-2-1/3i)^3`
`=-(2+1/3i)^3`
[Using, `(a+b)^3=a^3+b^3+3ab(a+b)`]
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RD SHARMA-COMPLEX NUMBERS-Solved Examples And Exercises
  1. Express each of the following in the form a+i b :(1/3+3i)^3

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  2. Express each of the following in the form a+i b :(5-3i)^2

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  3. Express each of the following in the form a+i b :(-2-1/3i)^3

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  4. Express each of the following in the form a+i b :(-sqrt(3)+\ sqrt(-2))...

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  5. Express the following in the standard form a+i b :1/(3-4i)

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  6. Express the following in the standard form a+i b :((3-2i)(2+3i))/((1+2...

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  7. Express the following in the standard form a+i b :(5+4i)/(4+5i)

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  8. Express the following in the standard form a+i b :1/(-2+sqrt(-3))

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  9. Express the following in the standard form a+i b :((3+isqrt(5))(3-isqr...

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  10. Express the following in the standard form a+i b :((1+i)^2)/(3-i)

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  11. Express the following in the standard form a+i b :(1/(1-2i)+3/(1+i))((...

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  12. Express the following in the standard form a+i b :1/(1-costheta+2i sin...

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  13. Express (1-2i)^(-3) in the standard form a+i bdot

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  14. Perform the indicated operation and find the result in the form a+i b ...

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  15. Perform the indicated operation and find the result in the form a+i b ...

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  16. Multiply 3-2i by its conjugate.

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

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  18. Find the multiplicative inverse of the complex number: 3+2i

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  19. Find the multiplicative inverse of the following complex number: (2+sq...

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  20. 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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