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Consider the complex number z=(1+3i)/(1-...

Consider the complex number `z=(1+3i)/(1-2i)`.Write z in polar form.

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A N EXCEL PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK
  1. Reduce (1/(1-4i) - 2/(1+i)) ((3-4i)/(5+i)) to the standard form

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

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  4. Consider the complex number z=(1+3i)/(1-2i).Write z in polar form.

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

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

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  7. Solve the following equations 27x^2-10x+1=0

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

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  9. If z1=2-i,z2=1+i Hence find abs[(z1+z2+1)/(z1-z2+i)]

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

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  12. Let z1=2-i, z2=-2+i. Find Im (1/(z1overlinez1))

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

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

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

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

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

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  18. Find the number of non zero integral solutions of the equation abs(1-i...

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  19. If (a+ib) (c+id) (e+if) (g+ih) = A+iB, then show that (a^2+b^2) (c^2+d...

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  20. If ((1+i)/(1-i))^m = 1 then find the least integral value of m

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