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If x+i y=(1+i)(1+2i)(1+3i),\ t h e n\ x^...

If `x+i y=(1+i)(1+2i)(1+3i),\ t h e n\ x^2+y^2` is a. `0` b. `1` c. `100` d. none of these

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To solve the problem, we need to find the value of \( x^2 + y^2 \) given that \( x + iy = (1 + i)(1 + 2i)(1 + 3i) \). ### Step-by-Step Solution: 1. **Express the Complex Number**: \[ z = x + iy = (1 + i)(1 + 2i)(1 + 3i) \] ...
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RD SHARMA-COMPLEX NUMBERS-Solved Examples And Exercises
  1. If a=1+i , then a^2 equals A. 1-i B. 2i C. (1+i)(1-i) D. (i-1)

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  2. If (x+i y)^(1//3)=a+i b ,\ then\ x/a+y/b is a. 0 b. 1 c. -1 d. none o...

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  3. (sqrt(-2))(sqrt(-3)) is equal to A. sqrt(6) B. -sqrt(6) C. isqrt(6)...

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  4. The argument of (1-isqrt(3))/(1+isqrt(3)) is a. 60^@ b. 120^@ c. 210^@...

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  5. If z=((1+i)/(1-i)), then z^4 equals a. 1 b. -1 c. 0 d non of t...

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  6. If z=(1+2i)/(1-(1-i)^2), then arg(z) equals a. 0 b. pi/2 c. pi ...

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  7. If z=1/((2+3i)^2), then |z| is a. 1/13 b. 1/5 c. 1/12 d. n...

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  8. If z=1/((1-i)(2+3i)), then |z| is a. 1 b. 1/sqrt(26) c. 5/sqrt(...

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  9. If z=1-costheta+isintheta,\ t h e n\ |z| is a. 2sin(theta/2) b. 2cos(t...

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  10. If x+i y=(1+i)(1+2i)(1+3i),\ t h e n\ x^2+y^2 is a. 0 b. 1 c. 100 d. n...

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  11. If z=1/(1-cos theta-i sin theta), then Re(z) is a. 0 b. 1/2 c. c...

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  12. If x+i y=(3+5i)/(7-6i), then y is

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  13. The amplitude of 1/i is equal to-

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  14. The argument of (1-i)/(1+i) is-

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  15. The amplitude of (1+isqrt(3))/(sqrt(3)+i) is a. pi/3 b. -pi/3 c. pi/6 ...

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  16. (1+2i+3i^2)/(1-2i+3i^2) equals a. i b. -1 c. -i d. 4

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  17. The value of (i^(592)+i^(590)+i^(588)+i^(586)+i^(584))/(i^(582)+i^(580...

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  18. A real value of x satisfies the equation (3-4i x)/(3+4i x)=a-i b(a ,\ ...

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  19. The complex number which satisfies the condition |(i+z)/(i-z)|=1\ li...

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  20. If z is a complex number, then a. |z|^2>|z^2| b. |z|^2=|z^2| c. |z|^2<...

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