Question 641905: What is (3i)^4 + 1 in standard form a+bi
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! Review
i = sqrt(-1) = 1 @ 9o degrees
i^2 = (sqrt(-1))^2 = -1 = 1 @ 180 degrees
i^3 = i*(i^2) = i*(-1) = -i = 1 @ -90 degrees
i^4 = i^2*i^2 = (-1)(-1) = 1 = 1 @ 0 degrees
Your expression
(1) (3i)^4 + 1 =
(2) (3^4)*(i)^4 + 1 =
(3) 81*1 + 1 =
(4) 82
Comparing (4) to the standard complex number form, we have
(5) a + ib
(6) 82 + i(0)
Because i^4 is real, there isn't any imaginary term in (1), and b is zero.
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