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Let z be a complex number such that |(z-...

Let z be a complex number such that `|(z-5i)/(z+5i)|=1`, then show that z is purely real

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ICSE-COMPLEX NUMBERS-Exercise (C)
  1. Find the modulus of (1-i)^(-2) + (1+ i)^(-2)

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  2. If z= 6+8i, verify that |z|= |bar(z)|

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  3. If z= 6+8i, verify that -|z| le " Re " (z) le |z|

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  4. If z= 6+8i, verify that -|z| lt "Im" (z) lt |z|

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  5. If z= 6+8i, verify that z^(-1)= (bar(z))/(|z|^(2))

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

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

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

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

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

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  11. If z(1)=3 + 4i,z(2)= 8-15i, verify that |z(2)-z(1)| gt ||z(2)|- |z...

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

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  13. Find the modulus of the following using the property of modulus (3+...

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  14. Find the modulus of the following using the property of modulus (8+...

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  15. Find the modulus of the following using the property of modulus (3+...

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  16. Find the modulus of the following using the property of modulus ((2...

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  17. Let z be a complex number such that |(z-5i)/(z+5i)|=1, then show that ...

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  18. Find the complex number z satisfying the equation |(z-12)/(z-8i)|= (5)...

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  19. If z is a complex number such that |z-1|= |z+1|, show that Re(z)= 0

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  20. Solve |z|+z= 2+ i, where z is a complex number

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