2007-05-12 11:39:56 · 8 answers · asked by aradioactivefish 1 in Science & Mathematics ➔ Mathematics
1(-2)^4+4(-2)^3(2i)+6(-2)^2(2i)^2+4(-2)(2i)^3+1(2i)^4
16-32(2i)+(24)(4)(-1)-8(8i)-2
(16-96-2)+(64i-64i)
=-82
2007-05-12 11:50:11 · answer #1 · answered by tema 2 · 0⤊ 1⤋
First take out the 2 and change signs in the parentheses to get
16(1-i)^4.
First, let's get (1-i)².
We have 1-2i -1 = -2i
Thus, squaring again,
(1-i)^4 = -4,
so the answer is -64.
2007-05-12 21:42:18 · answer #2 · answered by steiner1745 7 · 0⤊ 0⤋
(-2+2i)^4
= (-2)^4(1 - i)^4
= 16(1 + i^2 - 2i)^2
= 16(-2i)^2
= 16(4i^2)
= -64.
2007-05-12 18:44:49 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Expand using the binomial theorem.
(-2 + 2i)^4 =
(-2)^4 + 4*((-2)^3)*(2i) + 6*((-2)^2)*(2i)^2 + 4*(-2)*(2i)^3 +
(2i)^4
Which is:
16 - 64i - 48 + 64i + 16 = -16
2007-05-12 18:50:02 · answer #4 · answered by qspeechc 4 · 0⤊ 1⤋
( -2 + 2i ) ^4 = ( -2 + 2 i )^2 ( -2 + 2 i )^2
= ( 4 - 8i -4 ) ( 4 -8 i - 4 )
= ( -8 i ) ( -8 i )
= -64
2007-05-12 18:52:59 · answer #5 · answered by muhamed a 4 · 0⤊ 0⤋
(-2+2i)^2 = -8i
(-2+2i)^4 = [(-2+2i)^2]^2 = (-8i)(-8i) = 64i^2 = -64
2007-05-12 18:50:20 · answer #6 · answered by Patrick G 1 · 0⤊ 0⤋
-64
(-2 + 2i)^4
(4 - 8i + 4i^2)^2
(4 - 8i - 4)^2
(-8i)^2
64i^2
-64
also, you could plug it into google calculator:
http://www.google.com/search?q=(-2%2B2i)%5E4&sourceid=navclient-ff&ie=UTF-8&rls=GGGL,GGGL:2006-27,GGGL:en
2007-05-12 18:44:55 · answer #7 · answered by eirikir 2 · 0⤊ 0⤋
-64
2007-05-12 18:49:00 · answer #8 · answered by tochau 5 · 0⤊ 0⤋