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If arg(z - 1) = pi/6 and arg(z + 1) = 2 ...

If `arg(z - 1) = pi/6` and `arg(z + 1) = 2 pi/3` , then prove that `|z| = 1`.

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`|z| = 1`
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FULL MARKS-COMPLEX NUMBERS -ADDITIONAL QUESTIONS SOLVED
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  2. Show that |(z-3)/(z + 3)| = 2 represent a circle

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  3. If arg(z - 1) = pi/6 and arg(z + 1) = 2 pi/3 , then prove that |z| = 1...

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  4. P represents the variable complex number z. Find the locus of P, if Im...

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  5. P represents the variable complex number z find the locus of z if : ...

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  6. Write the following complex numbers in the polar form : 1- i

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  7. Find the modulus and principal argument of (1 + i) and hence express i...

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  8. Express the following complex numbers in the polar form. (i) (1 + i)...

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  9. Express the following complex numbers in the polar form : 2 + sqrt(3) ...

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  10. Find the modulus and principal argument of the following complex numbe...

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  11. Express the following complex numbers in the polar form : -1 - i

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  12. Express the following complex numbers in the polar form : 1 - i

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  13. Evaluate i^(50)

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  14. Evaluate i^(59)

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  15. Prove that : (1 + i)^(4n) and (1 + i)^(4n + 2) are real and purely ima...

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  16. If x = cos alpha + i sin alpha , y = cos beta + i sin beta, prove that...

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  17. If a = cos 2alpha + i sin 2 alpha, b = cos 2 beta + i sin 2 beta and c...

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  18. Solve : x^4 + 4 = 0

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  19. If x = a + b, y = a omega + b omega^2, z = aomega^2 + b omega, show th...

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  20. ((1 - i)/(1+ i))^(100) = a + ib then (a,b) is ……….

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