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IrishBoy123
 one year ago
complex plane
IrishBoy123
 one year ago
complex plane

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IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1\(\huge (\frac{1 + i}{1i})^{2718}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1angle = \(45(45) = 90\) so thats simply \(\large e^{i\frac{\pi}{2}*2718}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0consider \(1+i=(1i)^*\) hence $$\frac1{1i}=\frac{(1i)^*}{\sqrt2}=\frac{1+i}{\sqrt2}$$ so $$\frac{1+i}{1i}=\frac1{\sqrt2}(1+i)^2=\sqrt2i$$

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ergo \((\sqrt2i)^{2718}=2^{1359}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0or it might actually have been \(2\) not \(\sqrt2\) in which case i meant \(i^{2718}=1\) since \(2718=2716+2\equiv2\pmod4\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0One could actually just perform the division too,\[\frac{ 1+i }{ 1i } \equiv \frac{(1+i)^2}{1^2  i^2} = i\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1looks irishboy cooked up the problem from \(e^{i\pi}=1\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\left\{ \frac{ 1+\iota }{ 1\iota } \times \frac{ 1+\iota }{ 1+ \iota } \right\}^{2718}\] \[=\left( \frac{ 1+\iota ^2+2 \iota }{ 1\iota ^2 } \right)^{2718}\] \[=(\frac{ 11+2 \iota }{ 1(1) })^{2718}\] \[=\left( \iota ^2 \right)^{1359}=\left( 1 \right)^{1359}=1\]

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1thanks everyone for the help!
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