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Standard XII

Mathematics

Distance Formula Using Complex Numbers

The number of...

Question

The number of complex numbers z satisfying |z - 2|= 2 and z(1 - i) + $¯ z$ (1 + i) = 4 is

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Solution

The correct option is B
2

$(z + ¯ z)$ + i $(¯ z - z)$ = 4 gives x + y = 2 (z = x + iy)

The line x + y = 2 cuts the circle $| z - 2 |$ = 2 only at two points

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Similar questions

Q. Let

z

be those complex number which satisfy

| z + 5 | \leq 4

and

z (1 + i) + ¯ z (1 - i) \geq - 10, i = \sqrt{- 1}

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α + β \sqrt{2}

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The number of complex numbers $z_{1}$ which can simultaneously satisfy both the equations $|$ z - 2 $|$ = 2 and z(1 - i) + $¯ z (1 + i)$ = 4 is equal to

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The number of complex numbers z satisfying |z - 2|= 2 and z(1 - i) + ¯z(1 + i) = 4 is

The correct option is B 2 (z+¯z) + i(¯z−z) = 4 gives x + y = 2 (z = x + iy) The line x + y = 2 cuts the circle |z−2| = 2 only at two points

The number of complex numbers z satisfying |z - 2|= 2 and z(1 - i) + $¯ z$ (1 + i) = 4 is

The correct option is B
2

$(z + ¯ z)$ + i $(¯ z - z)$ = 4 gives x + y = 2 (z = x + iy)

The line x + y = 2 cuts the circle $| z - 2 |$ = 2 only at two points