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Find the number of non-zero integral sol...

Find the number of non-zero integral solutions of the equation `|1-i|^x=2^xdot`

Text Solution

Verified by Experts

Given: `| 1 -i|^x = 2^x`
we know,
`|a + ib|` = `√(a² + b²)` use this concept here,
so, `|1 - i|` =` √{1² + (-1)²}` = `√(1 + 1) = √2`
now,
...
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  3. Find the number of non-zero integral solutions of the equation |1-i|^...

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  4. Solve the equation: x^2 + x/sqrt2 + 1 =0

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  6. Convert of the complex number in the polar form: 1-i

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  7. Let z1=2-i ,z2=-2+i. Find (i) Re ((z1z2)/( bar z1)) (ii) Im(1/(z1 b...

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  8. Find the modulus and argument of the complex number (1+2i)/(1-3i).

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

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  10. If a + i b =((x+i)^2)/(2x^2+1),prove that a^2+b^2=((x^2+1)^2)/((2x^2+...

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  11. Convert of the complex number in the polar form: i

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  12. If alphaand betaare different complex numbers with |beta|=1,then fin...

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  13. Find the real numbers x and y if (x-i y)(3+5i) is the conjugate of -6...

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

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  15. Convert of the complex number in the polar form: -1-i

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  16. Find the modulus and the arguments of the complex number z = - 1 - is...

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  17. Find the modulus and the arguments of the complex number z=-sqrt(3)+i

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  18. Convert the complex number z=(i-1)/(cospi/3+isinpi/3)in the polar form...

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  19. Find real theta such that (3+2isintheta)/(1-2isintheta)is purely real...

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  20. If x + i y =(a+i b)/(a-i b),prove that x^2+y^2=1.

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