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If z=x+iy, show that sqrt(2)|z| ge |x|+ ...

If `z=x+iy`, show that `sqrt(2)|z| ge |x|+ |y|`.

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA
  1. Find the conjugate, modulus and amplitude of the complex number (sqrt(...

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  2. Find the modulus -amplitude fomr of the complex number (-2sqrt(3)-2i).

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  3. If z=x+iy, show that sqrt(2)|z| ge |x|+ |y|.

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  4. If the modulus of the complex number a+ib (b neo) is 1, showthat the c...

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  5. find the cube roots of i

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  6. If z(1), z(2),z(3),are three complex numbers, prove that z(1).Im(barz...

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  7. If omega be an imaginary cube root or unity, prove that (1)/(1+2 ome...

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  8. If omega be an imaginary cube root or unity, prove that (x+y omega+...

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  9. If omega be an imaginary cube root or unity, prove that (1- omega+ o...

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  10. Prove that ((-1+sqrt(-3))/(2))^(n)+((-1-sqrt(-3))/(2))^(n) =2, when...

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  11. If m, n and p are arbitrary integers, show that the equation x^(3m)+x^...

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  12. The sides of a right angled triangle are in A.P. ,' show that the side...

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  13. The sum of first p terms of an A.P. is zero. Show that the sum of a n...

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  14. If a(1),a(2),...a(k) are in A.P. then the equation (S(m))/(S(n))=(m^...

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  15. If f(x)=(1)/(x^(2)), show that f(x)-f(x+1)=(2m-1)/(x^(2)(x+1)^(2)), he...

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  16. Let t(p) be the p th term of an A.P. if its n th tem is zero, show tha...

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  17. Let a,b,c,d, be four quantities such that a+c=2 b and ab+cd+ad=3bc(b n...

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  18. Does there exist a geometric progression containing 27, 8 and 12 as th...

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  19. If a=2 and e=18 , then find three numbers b,c,d betweem a and e such t...

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  20. Prove that any sequence of numbers a(1),a(2),...a(n) satisfying the co...

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