Comple number q. (2 Viewers)

[spikestar]

i cant figure this out:
a) factorise z^4+64 into linear factors over c
b) factorise z^4+64 over r

 

[Mill]

Remember how there is no formula for the sum of two squares?!

Make it into a difference of two squares!

z⁴ + 64 = 0

(z²)² - (8i)² = 0

(z² - 8i)(z² + 8i) = 0

From here, there are a few ways you could go, but I'll leave that to you!


Alternatively, you could convert -64 into mod-form and use De Moivre's theorem to find the fourth roots. This second method is probably more familiar to most students.

 

[spikestar]

the thing you showed me i already done but i'm not clear on what to do from there.

Alternatively, you could convert -64 into mod-form and use De Moivre's theorem to find the fourth roots. This second method is probably more familiar to most students.

i dont understand that

 

[SeDaTeD]

means z^4 = 64 cis((2k+1)pi), where k is an integer. Then solve for z.

 

[spikestar]

1 more thing that has not been answered what does over R mean?

 

[webby234]

over the real numbers - eg (x^2 +1) rather than (x-i)(x+i)