Simple Complex Numbers Q (1 Viewer)

[mathshelp]

(1+i)^8

I keep getting 16 but I know that cannot be right.

 

[Shadowdude]

Show us your working.

 

[ohexploitable]

16 is correct.

 

[ohexploitable]

but I know that cannot be right.

lols, why would you think this?

 

[mathshelp]

= 1 + 8i + 28i^2 + 56i^3 + 70i^4 + 56i^5 + 28i^6 + 8i^7 + i^8
= 1 + 8i - 28 - 26i + 70 + 56i -28 -8i + 1
= 16

 

[ohexploitable]

= 1 + 8i + 28i^2 + 56i^3 + 70i^4 + 56i^5 + 28i^6 + 8i^7 + i^8
= 1 + 8i - 28 - 26i + 70 + 56i -28 -8i + 1
= 16

lols, no need to expand, just go:

 

[Shadowdude]

= 1 + 8i + 28i^2 + 56i^3 + 70i^4 + 56i^5 + 28i^6 + 8i^7 + i^8
= 1 + 8i - 28 - 26i + 70 + 56i -28 -8i + 1
= 16

56i^3 = 56i . i^2 = -56i

How did you get -26i?

 

[Drongoski]

= 1 + 8i + 28i^2 + 56i^3 + 70i^4 + 56i^5 + 28i^6 + 8i^7 + i^8
= 1 + 8i - 28 - 26i + 70 + 56i -28 -8i + 1
= 16

Easier this way:





Edit:

ohexploitable faster @ LaTeX than me!

 

[gurmies]

(1+i)^8

I keep getting 16 but I know that cannot be right.

SURELY the power of a complex number with real and imaginary parts cannot possibly end up purely real!?!? i^4 = ?

 

[rawrence]

SURELY the power of a complex number with real and imaginary parts cannot possibly end up purely real!?!? i^4 = ?

i^4 = 1? eh? I dont understand why it can't end up purely real

 

[tommykins]

ew cis

 

[ZachBC_94]

SURELY the power of a complex number with real and imaginary parts cannot possibly end up purely real!?!? i^4 = ?

Same way cis(2pi/3) is one of the points on the unit circle z^3 = 1