Evaluate the expression (3i)^4 and write the results in the form a+ bi.
a. -81
b. -16
c. 4
d. 16
e. 81
2007-09-07 06:26:22 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
e. 81 (though in a + bi form, it would be 81 + 0i)
(3i)^4 = 3i * 3i * 3i * 3i = (3i * 3i) * (3i * 3i) = 9i^2 * 9i^2. Since i is the square root of -1, i^2 is -1. So: 9*(-1)^2 * 9*(-1)^2 = (9*1) * (9*1) = 9 * 9 = 81. Put into a + bi form, it is 81 + 0i.
2007-09-07 06:33:52 · answer #1 · answered by bimeateater 7 · 0⤊ 0⤋
That's 3^4* i^4.
But 3^4 = 81 and i ^4 = 1(since i² = -1)
So the answer is 81.
2007-09-07 07:44:46 · answer #2 · answered by steiner1745 7 · 0⤊ 0⤋
answer e
i^4 = 1
3^4 = 81
answer = (81)(1) = 81
correct form
81 + 0i
2007-09-07 07:00:20 · answer #3 · answered by 037 G 6 · 0⤊ 0⤋
i^2 = -a million i^4 = ( i^2 )^2 = ( - a million )^2 = a million now i^( 1002 ) = i^2 * i^(1000 ) ..............= -a million ( i^4 )^( 250 ) .............= -a million ( a million )^( 250 ) .............= -a million * a million = -a million .............= -a million + i * 0
2016-11-14 10:35:05 · answer #4 · answered by deily 4 · 0⤊ 0⤋