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Suppose z = x + iy and w = (1-iz)/(z-i) ...

Suppose z = x + iy and w = `(1-iz)/(z-i)` Find `absw`. If `absw` = 1, prove that z is purely real

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The correct Answer is:
`(sqrt(1+y)^2+x^2)/(sqrt(x^2+(y-1)^2)`
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A N EXCEL PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK
  1. Suppose z1 = 1 - i and z2 = -2 + 4i Joseph evaluted abs((z1z2)/z1) usi...

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  2. Suppose z = x + iy and w = (1-iz)/(z-i) Find 1 - iz and z - 1 in the s...

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  3. Suppose z = x + iy and w = (1-iz)/(z-i) Find absw. If absw = 1, prove...

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  4. Consider the complex number z1 = 2 - i and z2 = -2 + i Find (z1z2)/z1...

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  5. Consider the complex number z1 = 2 - i and z1 = -2 + i Raju prove tha...

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  6. Consider the complex number z1 = 2 - i and z2 = 2 + i Find 1/(z1z2). ...

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  7. Given that for any complex number z, absz^2 = zoverlinez . Prove that ...

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  8. Given that for any complex number z, absz^2 = zoverlinez . Prove that ...

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  9. Represent the following complex numbers as points in the argand plane ...

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  10. Represent the following complex numbers as points in the argand plane ...

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  11. Represent the following complex numbers as points in the argand plane ...

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  12. Represent the complex number z=1+i in the polar form.

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  13. Represent each of the following numbers in polar form. -sqrt3 + i

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  14. Represent each of the following numbers in polar form. 4i

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  15. Find the modulus-amplitude form of the complex number (1+7i)/(2-i)^2

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  16. Prove that (cos45^@ + isin45^@)^2 = i

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  17. Represent the quotient (7(cos((3pi)/4)+isin((3pi)/4)))/(21(cos(pi/4)+i...

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  18. Show that the points representing the complex numbers 3+2i, 2-i and -7...

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  19. Find the modulus and argument of the following complex number z = -1 ...

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  20. Represent each of the following numbers in polar form. -sqrt3 + i

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