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If z is a complex number, then a. |z|^2>...

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

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Given: `z` is a complex number.
Now.
Let `z=x+i y`
then `|z|^{2}=(|x+i y|)^{2}`
`Rightarrow|z|^{2}=(.sqrt{x^{2}+y^{2}}|^{2}`.
`Rightarrow|z|^{2}=x^{2}+y^{2}-(2)`
Now,
`|z^{2}| =|(x+i y)^{2}|`
...
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RD SHARMA-COMPLEX NUMBERS-Solved Examples And Exercises
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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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  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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