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If |z(1)|=|z(2)|, "is it necesssary that...

If `|z_(1)|=|z_(2)|, "is it necesssary that "z_(1) = z_(2)`.

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If z_(1) and z_(2) are two complex numbers such that |z_(1)|= |z_(2)| , then is it necessary that z_(1) = z_(2)

If z_(1)=3 + 4i,z_(2)= 8-15i , verify that |z_(1) + z_(2)| lt |z_(1)| + |z_(2)|

If z_(1)=3 + 4i,z_(2)= 8-15i , verify that |z_(1) + z_(2)|^(2) + |z_(1)-z_(2)|^(2)= 2(|z_(1)|^(2) + |z_(2)|^(2))

If |z_(1)|= |z_(2)|= ….= |z_(n)|=1 , prove that |z_(1) + z_(2) + …+ z_(n)|= |(1)/(z_(1)) + (1)/(z_(2)) + …(1)/(z_(n))|

If |z_(1)|=|z_(2)|=1 , then prove that [{:(,z_(1),-z_(2)),(,bar(z)_(2),bar(z)_(1)):}] [{:(,bar(z)_(1),z_(2)),(,-bar(z)_(2),z_(1)):}]=[{:(,1//2,0),(,0,1//2):}]

If z_(1)=3 + 4i,z_(2)= 8-15i , verify that |z_(1)z_(2) |= |z_(1)| |z_(2)|

If the complex numbers z_(1), z_(2), z_(3) represent the vertices of an equilateral triangle, and |z_(1)|= |z_(2)| = |z_(3)| , prove that z_(1)+ z_(2) + z_(3)=0

If z_(1)=2 + 7i and z_(2)=1- 5i , then verify that |z_(1)z_(2)|= |z_(1)||z_(2)|

If z_(1)=3 + 4i,z_(2)= 8-15i , verify that |(z_(1))/(z_(2))|= (|z_(1)|)/(|z_(2)|)

If z_(1)=2 + 7i and z_(2)=1- 5i , then verify that |z_(1) + z_(2)| le |z_(1)| + |z_(2)|

VMC MODULES ENGLISH-COMPLEX NUMBERS -JEE ARCHIVE
  1. If |z(1)|=|z(2)|, "is it necesssary that "z(1) = z(2).

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  2. A complex number z is said to be unimodular if abs(z)=1. Suppose z(1) ...

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  3. If z is a complex number such that |z|geq2 , then the minimum value...

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  4. Let complex numbers alpha and 1/alpha lies on circle (x-x0)^2+(y-y0)^2...

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  5. Let z be a complex number such that the imaginary part of z is nonz...

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  6. Let z = x + iy be a complex number where x and y are integers. Then...

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  7. If |z|=1a n dz!=+-1, then all the values of z/(1-z^2) lie on a line no...

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  8. If w=alpha+ibeta, where beta!=0 and z!=1 , satisfies the condition tha...

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  9. If |z|=1 and w=(z-1)/(z+1) (where z!=-1), then R e(w) is 0 (b) 1/(|...

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  10. about to only mathematics

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  11. about to only mathematics

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  12. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

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  13. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

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  14. Let A,B and C be three sets of complex numbers as defined below: {:(,A...

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  15. Let A,B and C be three sets of complex numbers as defined below: {:(,A...

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  16. Let A,B and C be three sets of complex numbers as defined below: {:(,A...

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  17. about to only mathematics

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  18. If z is complex number of unit modulus and argument theta then arg ...

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  19. Let z(1) and z(2) be two distinct complex numbers and z=(1-t)z(1)+tz(2...

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  20. A particle P starts from the point z0=1+2i , where i=sqrt(-1) . It mov...

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  21. A man walks a distance of 3 units from the origin towards the North-...

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