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Express each of the following in the s...

Express each of the following in the standerd from ` a + ib`
`(2+3i)/(3+ 2i)`

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CENGAGE PUBLICATION-COMPLEX NUMBERS-ILLUSTRATION
  1. Evaluate : i^(75)

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  2. Evaluate : i^(103)

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  3. Express each of the following in the standerd from a + ib (2+3i)...

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  4. Find the value of (1+ i)^(6) + (1-i)^(6)

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

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  6. Prove that the triangle formed by the points 1,(1+i)/(sqrt(2)),and i a...

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  7. Find real q such that (3+2isintheta)/(1-2isintheta) is purely real.

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  8. If the imaginary part of (2z+1)//(i z+1) is -2, then find the locus of...

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  9. If z is a complex number such that |z - barz| +|z + barz| = 4 then fi...

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  10. If (x+i y)^5=p+i q , then prove that (y+i x)^5=q+i pdot

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  11. If z = x + iy lies in the third quadrant, then prove that (barz)/(z) ...

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  12. Let z = ((sqrt(3))/(2) + (i)/(2))^(5)+((sqrt(3))/(2)-(i)/(2))^(5). If ...

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  13. Find the relation if z1, z2, z3, z4 are the affixes of the vertices of...

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  14. Let z1, z2, z3 be three complex numbers and a ,b ,c be real numbers no...

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  15. Find real values of x and y for which the complex numbers -3+i x^2y an...

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  16. about to only mathematics

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

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  18. Let z be a complex number satisfying the equation z^2-(3+i)z+m+2i=0,w ...

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  19. Show that the equation Z^4+2Z^3+3Z^2+4Z+5=0 has no root which is eithe...

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  20. Find the square root of the following: 5+12 i

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