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Find the real values of x\ a n d\ y ,\ i...

Find the real values of `x\ a n d\ y ,\ if:(x+i y)(2-3i)=4+i`

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To solve the equation \((x + iy)(2 - 3i) = 4 + i\), we will follow these steps: ### Step 1: Expand the left-hand side We start by multiplying the two complex numbers on the left side: \[ (x + iy)(2 - 3i) = x \cdot 2 + x \cdot (-3i) + iy \cdot 2 + iy \cdot (-3i) \] This simplifies to: ...
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RD SHARMA-COMPLEX NUMBERS-Solved Examples And Exercises
  1. Express the following complex numbers in the standard form a+i b :(3-4...

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  2. Express the following complex numbers in the standard form a+i b :(5+s...

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  3. Find the real values of x\ a n d\ y ,\ if:(x+i y)(2-3i)=4+i

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  4. Find the real values of x\ a n d\ y ,\ if:((1+i)x-2i)/(3+i)+((2-3i)y+i...

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  5. Find the real values of x\ a n d\ y ,\ if:(3x-2iy)(2+i)^2=10(1+i)

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  6. Find the real values of x\ a n d\ y ,\ if:(1+i)(x+i y)=2-5i

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  7. Find the conjugates of the following complex number: 4-5i

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  8. Find the conjugates of the following complex number: 1/(3+5i)

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  9. Find the conjugates of the following complex number: 1/(1+i)

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  10. Find the conjugates of the following complex number: ((1+i)(2+i))/(3+i...

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  11. Find the conjugates of the following complex number: ((3-i)^2)/(2+i)

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  12. Find the conjugates of the following complex number: ((3-2i)(2+3i))/((...

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  13. Find the multiplicative of the following complex number: 1-i

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  14. Find the multiplicative of the following complex number: \ 4-3i

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  15. Find the multiplicative of the following complex number: (1+isqrt(3))^...

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  16. Find the multiplicative of the following complex number: sqrt(5)+3i

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  17. If z1=2-i ,\ z2=1+i , find |(z1+z2+1)/(z1-z2+i)|.

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  18. If z1=2-i ,\ z2=-2+i , find : R e((z1z2)/bar(z1))

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  19. If z1=2-i ,\ z2=-2+i , find : Im(1/(z1bar(z1))).

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  20. Find the modulus of (1+i)/(1-i)-(1-i)/(1+i)

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