Discussion in 'Mathematics' started by Xrnrdp, Jun 12, 2018.
Can someone show me a step by step how to factor z^4+64
If dealing with only real numbers, the expression is fully simplified. If imaginary numbers are permitted, there is more that can be done.[ z^4+64 ] is the same as [z^4 — (-64) ]Conjugate pairs multiply as a difference of squares, ie. An expression in the form (a + b) (a-b) multiplies out as a² — b².√ (-64)=8 i, where i is an imaginary number with the value √ (-1) So: z^4+64=z^4 — (-64)=(z²+8 i) (z² — 8 i) After this, it gets extremely messy due to the value of √ (i) being interestingly complex on its own, since √ (i)=√ (0,5)+√ (0,5) i
Separate names with a comma.