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Properties of Modulus

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Question

How solve and what is its meaning
$z_{1} = 2 + 3 i$
$z_{2} = 3 + 4 i$
$| z_{1} + z_{2} | = ?$

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Solution

$z_{1} = 2 + 3 i$
$z_{2} = 3 + 4 i$

$⟹ z_{1} + z_{2} = 5 + 7 i$

$∴ | z_{1} + z_{2} | = \sqrt{5^{2} + 7^{2}} = \sqrt{25 + 49} = \sqrt{74}$

It is modulus of a complex number

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z_{1} = 1 + 2 i, z_{2} = 2 + 3 i, z_{3} = 3 + 4 i

z_{1}, z_{2}

z_{3}

z_{1} = 1 + 2 i, z_{2} = 2 + 3 i, z_{3} = 3 + 4 i,

z_{1}, z_{2}

z_{3}

represent the vertices of

z_{1} = 3 + 4 i

z_{2} = - 4 + 3 i

. Then the modulus of

z = z_{1} + z_{2}

z_{1} = 2 + 3 i

z_{2} = 3 + 4 i

be two points on the complex plane. Then, the set of complex number

z

{| z - z_{1} |}^{2} + {| z - z_{2} |}^{2} = {| z_{1} - z_{2} |}_{1}^{2}

Z_{1} = 2 + 3 i

z_{2} = 3 + 4 i

be two points on the complex plane. Then the set of complex numbers z satisfying

| z - z_{1} |^{2} + | z - z_{2} |^{2} = | z_{1} - z_{2} |^{2}

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