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Consider the complex number (i-1)/(cos...

Consider the complex number
`(i-1)/(cosfrac(pi)(3)+isinfrac(pi)(3)`
Convert into polar form.

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V PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK

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  2. Find real theta such that (3+2 i sin theta)/(1-2 i sin theta) is purel...

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  3. Consider the complex number (i-1)/(cosfrac(pi)(3)+isinfrac(pi)(3) ...

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  4. Evaluate [i^18+(1/i)^25]^3

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  5. For any two complex numbers z1 and z2 prove that Re(z1z2) = Re(z1)Re(...

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  6. Reduce (1/(1-4i) - 2/(1+i)) ((3-4i)/(5+i)) to the standard form

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  7. If x-iy=sqrt((a-ib)/(c-id), prove that (x^2+y^2)^2 = (a^2+b^2)/(c^2+d^...

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  8. Convert the following in to the polar form (1+7i)/(2-i)^2

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  9. Solve the following equations 3x^2-4x+20/3=0

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  10. Solve the following equations x^2-2x+3/2=0

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  11. Solve 27 x^(2)-10 x+1=0

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  12. Solve the equation 21x^2-28x+10=0

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  13. If (z)(1)=2-i, (z)(2)=1+i, find |((z)(1)+(z)(2)+1)/((z)(1)-(z)(2)+1)|

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  14. If a+ib=(x+i)^2/(2x^2+1), prove that a^2+b^2=(x^2+1)^2/(2x^2+1)^2

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  15. Let z1=2-i, z2=-2+i. Find Re((z1z2)/overlinez1)

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  16. Find the modulus and argument of the complex number (1+2i)/(1-3i)

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  17. Find the real numbers x and y if (x-iy)(3+5i) is the conjugate of - 6 ...

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

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  19. If (x+iy)^3 = u + iv, then show that u/x+v/y=4(x^2-y^2)

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  20. If alpha and beta are different complex numbers with absbeta = 1, then...

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