Explain how to multiply complex numbers and give an example.

Question

Anahi Pearson · Accepted Answer

Concept - Every complex number has a real part and an imaginary part.
In order to multiply two complex numbers, we multiply real part of first complex number with the real and imaginary part of second complex number,
and we then multiply imaginary part of first complex number with the real and imaginary part of second complex number.
The resultant gives the multiplication of two complex numbers.We need to note that,
$i = ι = \sqrt{- 1}$ (It's presence represents the complex number)
And,
$i^{2} = i \times i + \sqrt{- 1} \times \sqrt{- 1} = - 1$
Hence,
$i^{2} = - 1$
This is we need to remember always.
Example -
Let two complex numbers be -
$z_{1} = 2 + 3 i$
$z_{2} = 1 + 2 i$
Now multiplying them -
$z_{1} \times z_{2} = (2 + 3 i) \times (1 + 2 i)$
$z_{1} \times z_{2} = (2 \times 1) + (2 \times 2 i) + (3 i \times 1) + (3 i \times 2 i)$
$z_{1} \times z_{2} = 2 + 4 i + 3 i + 6 i^{2}$
$z_{1} \times z_{2} = 2 + 7 i + 6 (- 1)$
$z_{1} \times z_{2} = 2 + 7 i - 6$
$b f z_{1} \times z_{2} = - 4 + 7 i$

Explain how to multiply complex numbers and give an example.

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