簡約 (e^{iax})/((z^2+b^2)^2)

解

簡約

\frac{e ^{ia x}}{( z ^{2} + b ^{2} ) ^{2}}

\frac{cos ( a x )}{b ^{4} + z ^{4} + 2 b ^{2} z ^{2}} + i \frac{sin ( a x )}{b ^{4} + z ^{4} + 2 b ^{2} z ^{2}}

解答ステップ

\frac{e ^{ia x}}{( z ^{2} + b ^{2} ) ^{2}}

e^{ia x} = cos (a x) + i sin (a x)

= \frac{cos ( a x ) + i sin ( a x )}{( z ^{2} + b ^{2} ) ^{2}}

標準的な複素数形式で

\frac{cos ( a x ) + sin ( a x ) i}{( z ^{2} + b ^{2} ) ^{2}}

を書き換える:

\frac{cos ( a x )}{z ^{4} + 2 b ^{2} z ^{2} + b ^{4}} + \frac{sin ( a x )}{z ^{4} + 2 b ^{2} z ^{2} + b ^{4}} i

= \frac{cos ( a x )}{z ^{4} + 2 b ^{2} z ^{2} + b ^{4}} + \frac{sin ( a x )}{z ^{4} + 2 b ^{2} z ^{2} + b ^{4}} i