I am supposed to write (1+i)^(1/2) to its polar form. However, I fail to get the right result. I always get a wrong angle. I don't know how to proceed.
#Complex numbers in their polar form
orchid zephyr
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orchid zephyr
This is how I calculated the length:
pseudo shadowBOT
Fischstaebchen
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orchid zephyr
Normally I'd calculate the angle using $arctan\left(\frac{y}{x}\right)$ but that doesn't lead to the expected result $\frac{\pi}{8}$ or 22.5°
pseudo shadowBOT
Fischstaebchen
orchid zephyr
If you reply please ping me otherwise I might not see it.
orchid zephyr
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steady cedar
Normally I'd calculate the angle using $arctan\left(\frac{y}{x}\right)$ but that...
@orchid zephyr u should use arctan(y/x) instead of tan(y/x).
orchid zephyr
whoops sorry I meant arctan
steady cedar
Can u show ....whatever u have worked out ?
orchid zephyr
I tried it this way:
pseudo shadowBOT
Fischstaebchen
orchid zephyr
but I didn't get the right result with that
I got 32.7651° instead of the expected 25.5°
quiet copper
Can't you just find the angle of 1+i and half the result ?
That's certainly easier
And 22.5° shows up easily this way
orchid zephyr
yeah but why can I simply half it ?
quiet copper
arg(z^2) = 2 arg(z), cause arg works nicely with products of complex numbers
But yeah you'd have to be wary which square root you take tbh
Cause the two square roots of 1+i certainly don't have the same argument
solemn cargo
I would go directly to polar first, then compute the root $$1+i= \sqrt{2}e^{i \frac{\pi}{4}}$$
$$(1+i)^{1/2} = \sqrt[4]{2}e^{i \frac{\pi}{8}}$$
pseudo shadowBOT
Merosity
