If z = x + iy, define the exponential of z, denoted eº, by e := e" e° (cos(y) + i sin(y)) . Prove that if z = reio (r > 0 and 0 E R) then one has lei| = e=rsin0. Evaluate ei| when 6ein/3. Z =

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If z = x + iy, define the exponential of z, denoted e², by
e := e® eiy
e (cos(y) + i sin(y)).
Prove that if z = rei0 (r > 0 and 0 E R) then one has |e?| = e-r sinº. Evaluate |e| when
6eiT/3.
= Z
Transcribed Image Text:If z = x + iy, define the exponential of z, denoted e², by e := e® eiy e (cos(y) + i sin(y)). Prove that if z = rei0 (r > 0 and 0 E R) then one has |e?| = e-r sinº. Evaluate |e| when 6eiT/3. = Z
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