Solved: "Find the following complex limits. limn→∞6n2n−n2i"

Yulia

Answered question

2021-02-02

Find the following complex limits.

lim_{n \to \infty} \frac{6 n}{2 n - n^{2} i}

Jaylen Fountain

Skilled2021-02-03Added 169 answers

lim_{n \to \infty} \frac{6 n}{2 n - n^{2} i} = lim_{n \to \infty} \frac{6}{2 n - n i}

Rationalize

\frac{6}{2 - n i}

\frac{6}{2 - n i} = \frac{6}{2 - n i} \cdot \frac{2 + n i}{2 + n i}

= \frac{12 + 6 n i}{4 - n^{2} i^{2}}

= \frac{12 + 6 n i}{4 + n^{2}}

= \frac{\frac{12 + 6 n i}{n^{2}}}{\frac{4 + n^{2}}{n^{2}}}

= \frac{\frac{12}{n^{2}} + \frac{6}{n i}}{\frac{4^{2}}{n^{2}} + 1}

Substitute

\frac{6}{2 - n i} = \frac{12}{n^{2}} + \frac{\frac{6}{n i}}{\frac{(4^{2})}{n^{2} + 1}}

= \frac{0 + 0 i}{(0 + 1)}

= 0

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