1285/8-60i=10^6M^2

解

\frac{1285}{8} - 60 i = 1 0^{6} M^{2}

M = \frac{257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}}{800 5} - \frac{3}{25 5 257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}} i, M = - \frac{257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}}{800 5} + \frac{3}{25 5 257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}} i

解答ステップ

\frac{1285}{8} - 60 i = 1 0^{6} M^{2}

代用

M = x + y i

\frac{1285}{8} - 60 i = 1 0^{6} (x + y i)^{2}

拡張

1 0^{6} (x + y i)^{2} : (1000000 x^{2} - 1000000 y^{2}) + 2000000 i x y

\frac{1285}{8} - 60 i = (1000000 x^{2} - 1000000 y^{2}) + 2000000 i x y

複素数は, その実数部と虚数部が等しい場合にのみ等しくなるequation系として書き換える:

[\frac{1285}{8} = 1000000 x^{2} - 1000000 y^{2} - 60 = 2000000 x y]

[\frac{1285}{8} = 1000000 x^{2} - 1000000 y^{2} - 60 = 2000000 x y] : x = \frac{257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}}{800 5}, x = - \frac{257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}}{800 5}, y = - \frac{3}{25 5 257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}} y = \frac{3}{25 5 257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}}

代用を戻す

M = x + y i

M = \frac{257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}}{800 5} - \frac{3}{25 5 257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}} i, M = - \frac{257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}}{800 5} + \frac{3}{25 5 257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}} i