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Solve the equation |z|=z+1+2idot...

Solve the equation `|z|=z+1+2idot`

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`|z|= z+1 + 2i`
`rArr sqrt(x^(2) + y^(2)) = x + iy + 1+ 2i =x+1+(2+y)i`
`rArr sqrt(x^(2) + y^(2)) = x + 1 and 0=2 +y or y = -2`
`rArr sqrt(x^(2) + 4)) = x+1`
`or x^(2) + 4 = x^(2) + 2x + 1`
`or 2x = 3`
`or x=(3)/(2)`
`rArr x + iy = (3)/(2)-2i`
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CENGAGE PUBLICATION-COMPLEX NUMBERS-ILLUSTRATION
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  3. Solve the equation |z|=z+1+2idot

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  4. Find the range of real number alpha for which the equation z+alpha|z-1...

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  9. Find the real part of (1-i)^(-i)dot

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  10. If (sqrt(8)+i)^(50)=3^(49)(a+i b) , then find the value of a^2+b^2dot

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  11. Show that (x^2+y^2)^4=(x^4-6x^2y^2+y^4)^2+(4x^3y-4x y^3)^2dot

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  17. It is given the complex numbers z(1) and z(2), |z(1)| =2 and |z(2)| ...

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