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Recent questions tagged exercise3-5

Find all the values of $\bigg(\large\frac{1}{2}$$-i\large\frac{\sqrt 3}{2}\bigg)^{\Large\frac{3}{4}}$ and hence prove that the product of the values is 1.

asked Jun 13, 2013 by sreemathi.v

1 answer

Solve : $x^4-x^3+x^2-x+1=0$

asked Jun 13, 2013 by sreemathi.v

1 answer

Solve : $x^4+4=0$

asked Jun 12, 2013 by sreemathi.v

1 answer

Prove that if $\omega^3=1$,then (iii) $\large\frac{1}{1+2\omega}-\frac{1}{1+\omega}+\frac{1}{2+\omega}$$=0$

asked Jun 12, 2013 by sreemathi.v

1 answer

Prove that if $\omega^3=1$,then (ii) $\bigg(\large\frac{-1+i\sqrt 3}{2}\bigg)^5+\bigg(\large\frac{-1-i\sqrt 3}{2}\bigg)^5$$=-1$

asked Jun 12, 2013 by sreemathi.v

1 answer

Prove that if $\omega^3=1$,then (i) $(a+b+c)(a+b\omega+c\omega^2)(a+b\omega^2+c\omega)=a^3+b^3+c^3-3abc$

asked Jun 12, 2013 by sreemathi.v

1 answer

If $x=a+b$,$y=a\omega+b\omega^2,z=a\omega^2+b\omega$ show that (ii) $x^3+y^3+z^3=3(a^3+b^3)$ where $\omega$ is the complex cube root of unity.

asked Jun 12, 2013 by sreemathi.v

1 answer

If $x=a+b$,$y=a\omega+b\omega^2,z=a\omega^2+b\omega$ show that (i) $xyz=a^3+b^3$ where $\omega$ is the complex cube root of unity.

asked Jun 12, 2013 by sreemathi.v

1 answer

Find all the value of the following : $(-\sqrt 3-i)^{\large\frac{2}{3}}$

asked Jun 12, 2013 by sreemathi.v

1 answer

Find all the value of the following : $(8i)^{\large\frac{1}{3}}$

asked Jun 12, 2013 by sreemathi.v

1 answer

Find all the value of the following : $(i)^{\large\frac{1}{3}}$

asked Jun 12, 2013 by sreemathi.v

1 answer

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