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MODERN PUBLICATION-COMPLEX NUMBERS-EXERCISE
- Find the square roots of the following : -8 - 6i.
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- Find the square roots of the following : 5-12i.
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- Find the square roots of the following : 3-4 sqrt7 i.
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- Find the square roots of the following : 4+6 sqrt(-5).
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- Find the square roots of the following : -2+2 sqrt3 i.
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- Prove that [4+ 3 sqrt(- 20)]^(1//2) +[4-3 sqrt(- 20)]^(1//2)= 6.
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- Evaluate : x^2+4x+7 when x =-2+ sqrt(-3).
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- Evaluate : 2x^3-9x^2-10x+13 when x =3+ sqrt(5).
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- Evaluate : x^4-3x^3+3x^2+99x-95 when x =3-4i.
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- If z1 = 5 + 7i and z2= 7 - 9i,verify : |-z1|=|z1|.
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- If z1 = 5 + 7i and z2= 7 - 9i,verify : |z1^2|=|z1|^2.
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- If z1 = 5 + 7i and z2= 7 - 9i,verify : |z1+z2| <|z1|+ |z2|.
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- If z1 = 5 + 7i and z2= 7 - 9i,verify : |z2-z1| > |z2|- |z1|.
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- If z1 = 5 + 7i and z2= 7 - 9i,verify : |z1 z2|=|z1| |z2|.
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- If z1 = 5 + 7i and z2= 7 - 9i,verify : |z1/z2|= (|z1|)/ (|z2|).
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- If z is any complex number, prove that : |z|^2= |z^2|.
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- If iz^3+z^2-z+i = 0, then show that |z|=1.
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- Find the non-zero integral solutions of |1-i|^x=2^x.
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- If |z1|=|z2|= ...... |zn|=1, prove that : |z1+z2+ ........ zn|= |1/z1...
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- If |z|=1, prove that (z-1)/(z+1) (z ne -1) is purely imaginary number....
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