How to find this using DeMoivre's Theorem? Express in standard form: (1 + i)^5
This is my work but the answer is wrong since it's suppose to be -4 - 4i....what did I do wrong?
z^5 = [√ 2^5 (cos(π/4 x 5)) + (isin(π/4 x 5))]
= 4√2 (cos 5π/4 + isin 5π/4 )
= 4√2 (-√2/2 + √2i/2)
=-4 + 4i
This is my work but the answer is wrong since it's suppose to be -4 - 4i....what did I do wrong?
z^5 = [√ 2^5 (cos(π/4 x 5)) + (isin(π/4 x 5))]
= 4√2 (cos 5π/4 + isin 5π/4 )
= 4√2 (-√2/2 + √2i/2)
=-4 + 4i
-
sin 5pi/4 = sin ( pi+ pi/4) = sinpicospi/4+ sinpi/4 cospi = 0+ (-1) sinpi/4 = -(1/2) sqrt2