Two complex numbers are represented by ordered pairs $z_{1} : (3, 4) & z_{2} : (4, 5)$ , which of the following is true for $z_{1} + z_{2}$ ?

z_{1} + z_{2} = (7, 9)

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z_{1} + z_{2} = (7 + 9 i)

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z_{1} + z_{2} = (1, 9)

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None of these

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Solution

The correct options are
A $z_{1} + z_{2} = (7, 9)$
D $z_{1} + z_{2} = (7 + 9 i)$
$z_{1} : (3, 4)$
$∴$ it can be written as $z_{1} = 3 + 4 i$
Also, $z_{2} : (4, 5)$
$∴$ it can be written as $z_{2} = 4 + 5 i$
$∴ z_{1} + z_{2} = 3 + 4 i + 4 + 5 i$
$\Rightarrow z_{1} + z_{2} = 7 + 9 i$
This can also be represented as $z_{1} + z_{2} = (7, 9)$
Hence, A and B are correct.

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