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

(- 3, 31)

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(- 8, 31)

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(- 1, 21)

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None of these

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Solution

The correct option is A $(- 8, 31)$
$z_{1} = 3 + 4 ι z_{2} = 4 + 5 ι z_{1} \times z_{2} = (3 + 4 ι) \times (4 + 5 ι) z_{1} \times z_{2} == 12 + 15 ι + 16 ι + 20 ι^{2} z_{1} \times z_{2} = 12 + 31 ι - 20 z_{1} \times z_{2} = - 8 + 31 ι$
So the point in the complex plane is $(- 8, 31)$
Option $B$ is correct

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