Let z 1- Z 2 be two complex numbers represented by points on the circle - z -3 and - z -4 respectively- thenA- max-3 z 1-2 z 2-17B- min- z 1- z 2-1C- - z 2-1- z 1- -13-3D- max-3 z 1-2 z 2-16

The correct options are A max|3z_1+2z_2|=17 B min|z_1 z_2|=1 C |z_2+1z_1|≤133|z_1|=3, |z_2|=4 |3z_1+2z_2|≤3|z_1|+2|z_2| =9+8=17 |z_1 z_2|≥||z_1| |z_2|| =|3 4| ...

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Byju's Answer

Standard XII

Mathematics

Distance Formula Using Complex Numbers

Let z 1, Z 2 ...

Question

Let $z_{1}, z_{2}$ be two complex numbers represented by points on the circle $| z | = 3$ and $| z | = 4$ respectively, then

max | 3 z_{1} + 2 z_{2} | = 17

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min | z_{1} - z_{2} | = 1

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∣ ∣ ∣ z_{2} + \frac{1}{z_{1}} ∣ ∣ ∣ \leq \frac{13}{3}

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max | 3 z_{1} + 2 z_{2} | = 16

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Solution

The correct options are
A $max | 3 z_{1} + 2 z_{2} | = 17$
B $min | z_{1} - z_{2} | = 1$
C $∣ ∣ ∣ z_{2} + \frac{1}{z_{1}} ∣ ∣ ∣ \leq \frac{13}{3}$
$| z_{1} | = 3, | z_{2} | = 4$

$| 3 z_{1} + 2 z_{2} | \leq 3 | z_{1} | + 2 | z_{2} |$
$= 9 + 8 = 17$

$| z_{1} - z_{2} | \geq | | z_{1} | - | z_{2} | |$
$= | 3 - 4 |$
$= 1$

$∣ ∣ ∣ z_{2} + \frac{1}{z_{1}} ∣ ∣ ∣ \leq | z_{2} | + ∣ ∣ ∣ \frac{1}{z_{1}} ∣ ∣ ∣$
$= | z_{2} | + \frac{1}{| z_{1} |}$
$= 4 + \frac{1}{3} = \frac{13}{3}$

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Similar questions

Q. Let

z_{1}

and

z_{2}

be any two non-zero complex numbers such that

3 | z_{1} | = 4 | z_{2} |

. If

z = \frac{3 z_{1}}{2 z_{2}} + \frac{2 z_{2}}{3 z_{1}}

then :

Q. If

θ_{1}

and

θ_{2}

are arguments of two non-zero complex numbers

z_{1}

and

z_{2}

respectively such that

3 | z_{1} | = 4 | z_{2} |

. If

z = \frac{3 z_{1}}{2 z_{2}} + \frac{2 z_{2}}{3 z_{1}}

, then

Q. Let

z_{1}

and

z_{2}

be any two non-zero complex numbers such that

3 | z_{1} | = 4 | z_{2} |

. If

z = \frac{3 z_{1}}{2 z_{2}} + \frac{2 z_{2}}{3 z_{1}}

then :

Q. If

θ_{1}

and

θ_{2}

are arguments of two non-zero complex numbers

z_{1}

and

z_{2}

respectively such that

3 | z_{1} | = 4 | z_{2} |

. If

z = \frac{3 z_{1}}{2 z_{2}} + \frac{2 z_{2}}{3 z_{1}}

then

Q. For any two complex numbers

z_{1}

and

z_{2},

| z_{1} | = 2

and

| z_{2} | = 3

then the value of

| 3 z_{1} + 2 z_{2} |^{2} + | 3 z_{1} - 2 z_{2} |^{2}

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Let z1, z2 be two complex numbers represented by points on the circle |z|=3 and |z|=4 respectively, then

The correct options are A max|3z1+2z2|=17 B min|z1−z2|=1 C ∣∣∣z2+1z1∣∣∣≤133|z1|=3, |z2|=4 |3z1+2z2|≤3|z1|+2|z2| =9+8=17 |z1−z2|≥||z1|−|z2|| =|3−4| =1 ∣∣∣z2+1z1∣∣∣≤|z2|+∣∣∣1z1∣∣∣ =|z2|+1|z1| =4+13=133

Let $z_{1}, z_{2}$ be two complex numbers represented by points on the circle $| z | = 3$ and $| z | = 4$ respectively, then