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If two complex numbers z1,z2 are such th...

If two complex numbers `z_1,z_2` are such that `|z_1|= |z_2|`, is it then necessary that `z_1 = z_2` ?

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MODERN PUBLICATION-COMPLEX NUMBERS-EXERCISE
  1. Find the absolute values and arguments of following complex numbers : ...

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  2. Find the absolute values and arguments of following complex numbers : ...

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  3. If two complex numbers z1,z2 are such that |z1|= |z2|, is it then nece...

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  4. Give the following in polar form : sin 120^@ -i cos 120^@.

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  5. Give the following in polar form : [2(cos 210^@ + i sin 210^@)] [4(c...

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  6. Give the following in polar form : [3(cos 225^@ + i sin 225^@)] [6(c...

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  7. Give the following quotients in polar form : (9(cos 90^@ + isin 90^@...

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  8. Give the following quotients in polar form : (7(cos 135^@ + isin 135...

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  9. Express the following in the polar form : 1+i.

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  10. Express the following in the polar form : -1 -i.

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  11. Express 1+isqrt3 in polar form.

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  12. Express the following in the polar form : (-16)/(1+ sqrt3 i).

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  13. Show that for z in C, |z|=0 if and only if z=0.

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  14. If z= x + iy, x, y real, prove that : |x|+|y| le sqrt2 |z|.

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  15. Define addition and multiplication of two complex numbers z1 and z2. H...

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  16. Define addition and multiplication of two complex numbers z1 and z2. H...

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  17. If z1,z2 in C, show that (z1+ z2)^2= z1^2+2 z1 z2+ z2^2.

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  18. Prove that |z1+ z2|^2= |z1|^2+ |z2|^2 if and only if (z1/z2) is purely...

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  19. Solve the following equation : x^2 +2=0.

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  20. Solve the following equation : x^2+x+1=0.

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