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If z1=7+3i and z2=-7+3i then find the fo...

If `z_1=7+3i` and `z_2=-7+3i` then find the following:
`z_1z_2`

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AI Generated Solution

To find the product of the complex numbers \( z_1 = 7 + 3i \) and \( z_2 = -7 + 3i \), we will follow these steps: ### Step 1: Write down the expression for the product We start with the expression for the product of the two complex numbers: \[ z_1 z_2 = (7 + 3i)(-7 + 3i) \] ...
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MAHAVEER PUBLICATION-COMPLEX NUMBERS-QUESTION BANK
  1. Find the modulus and amplitude of the following complex numbers: -1-i

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. If w is the imaginary cube root of unity evaluate |(1,w,w^2),(w,w^2,1...

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  16. If, x = 3 +i then find the value of the expression x^4-4x^3+4x^2-16x+6...

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  17. If x=1/sqrt2(1+i)then show that x^6+x^4+x^2+1=0

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  18. If z=cos30^@+isin30^@, find z^7

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  19. Show that, ((cos2theta+isin2theta)^3(cos3theta-isin3theta)^4)/((cos3th...

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  20. Find the values of (1+i)^(1/7)

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