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UkoKoshka [18]
4 years ago
11

Divide the following complex numbers (2 + i ) ÷ ( 1 - 4i ) ​

Mathematics
2 answers:
Dvinal [7]4 years ago
5 0

-2/17 + 9i/17 fractions

tiny-mole [99]4 years ago
3 0

Answer:

- \frac{2}{17} + \frac{9}{17} i

Step-by-step explanation:

Multiply the numerator/denominator by the complex conjugate of the denominator.

The conjugate of 1 - 4i is 1 + 4i

\frac{(2+i)(1+4i)}{(1-4i)(1+4i)} ← expand factors

= \frac{2+9i+4i^2}{1-16i^2} → i² = - 1

= \frac{2+9i-4}{1+16}

= \frac{-2+9i}{17}

= - \frac{2}{17} + \frac{9}{17} i

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