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Cramer's Rule

if im(z)=2 an...

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if im(z)=2 and z1=1+i then minimum value of |z-z1| is

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Q. If complex numbers

z_{1}

z_{2}

z + ¯ ¯ ¯ z = 2 | z - 1 |

arg (z_{1} - z_{2}) = \frac{π}{3},

then the value of

Im (z_{1} + z_{2})

Im (z)

denotes the imaginary part of

z

)

Q. If complex numbers

z_{1}

z_{2}

z + ¯ z = 2 | z - 1 |

arg (z_{1} - z_{2}) = \frac{π}{3},

then find the value of

Im (z_{1} + z_{2})

Im (z)

denotes the imaginary part of

z

)

Q. If complex numbers

z_{1}

z_{2}

z + ¯ z = 2 | z - 1 |

arg (z_{1} - z_{2}) = \frac{π}{3},

then find the value of

Im (z_{1} + z_{2})

Im (z)

denotes the imaginary part of

z

)

| Z - i | \leq 2

Z_{1} = 5 + 3 i

, then the maximum value of

| i Z + Z_{1} |

∣ ∣ \frac{z_{1} + z_{2}}{z_{1} - z_{2}} ∣ ∣ = 1

\frac{z_{1}}{z_{2}}

is purely imaginary
II. If z is purely real then

z = ¯ ¯ ¯ z

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