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Find the modulus of (3+4i)/(12+5i)...

Find the modulus of `(3+4i)/(12+5i)`

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To find the modulus of the complex number \((3 + 4i)/(12 + 5i)\), we can follow these steps: ### Step 1: Multiply by the Conjugate We start by multiplying the numerator and the denominator by the conjugate of the denominator. The conjugate of \(12 + 5i\) is \(12 - 5i\). \[ \frac{3 + 4i}{12 + 5i} \cdot \frac{12 - 5i}{12 - 5i} \] ...
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MAHAVEER PUBLICATION-COMPLEX NUMBERS-QUESTION BANK
  1. Find the conjugate of (2+3i)(3-4i)

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  2. Find the conjugate of (3+i)/(2+5i)

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  3. Find the modulus of (3+4i)/(12+5i)

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  4. Find the modulus and amplitude of the following complex numbers: sqrt3...

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  5. Find the modulus and amplitude of the following complex numbers: -4i

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  6. Find the modulus and amplitude of the following complex numbers: 1+isq...

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  7. Find the modulus and amplitude of the following complex numbers: -1-i

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  8. Find the additive and multiplicative inverse of -4+5i.

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  9. If z1=7+3i and z2=-7+3i then find the following: z1z2

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  10. If z1=7+3i and z2=-7+3i then find the following: barz1barz2

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  11. If z1=7+3i and z2=-7+3i then find the following: z1barz2

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  12. If z1=7+3i and z2=-7+3i then find the following: z1/z2

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  13. If z1=7+3i and z2=-7+3i then find the following: barz1/barz2

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  14. If x and y are real numbers of such that ((1+i)x-2i)/(3+i)+((2-3i)y+i...

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  15. Find the square root of 7-30sqrt(-2)

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  16. Find the square root of -3+4sqrt(-7)

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  17. Prove that, (1-w+w^2)^4+(1+w-w^2)^4=-16

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  18. Prove that (1+w)(1+w^2)(1+w^4)(1+w^8)=1 where w is the imagination cu...

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  19. If w be an imaginary cube root of unity, prove that (1-w+w^2)^2+(1+w-w...

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  20. Prove that (1-w+w^2)^5+(1+w-w^2)^5=32

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