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Fundamental Laws of Logarithms

If z1=2+3i an...

Question

If $z_{1} = 2 + 3 i$ and $z_{2} = 3 + 5 i$ , then $| z_{1} + z_{2} |$ represents:

A

The distance between

2 + 3 i

and

- 3 - 5 i

.

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B

None of the above.

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C

The distance between

2 + 3 i

and

3 + 5 i

.

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D

The distance between

- 2 - 3 i

and

3 + 5 i

.

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Solution

The correct option is D The distance between $- 2 - 3 i$ and $3 + 5 i$ .
$| z_{1} + z_{2} |$ can be written as $| z_{1} - (- z_{2}) |$ or can also be written as $| z_{2} - (- z_{1}) |$ , which means $| z_{1} + z_{2} |$ represents the distance between $z_{1}$ and $- z_{2}$ or the distance between $z_{2}$ and $- z_{1} .$

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Similar questions

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} = 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} = - 3 + 5 i; z_{2} = - 5 - 3 i

z

is a complex number lying on the line segment joining

z_{1}

z_{2}

a r g (z)

z_{1} = 2 - 5 i, z_{2} = 3 - i

, then magnitude of projection of

z_{1}

z_{2}

is .............

z_{1} = 1 + 2 i

z_{2} = 2 + 5 i

, then find the conjugate of

z_{1} + z_{2}

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