Unformatted text preview: z ∈ C ² ²  z  +  z4  = 8 ³ 5: For real numbers x and y , we deﬁne e x + iy = e x cos y + i e x sin y . For a complex number z , we deﬁne cos z = e iz + eiz 2 and sin z = e izeiz 2 i . (a) Show that for all z, w ∈ C we have e z + w = e z e w . (b) Show that for all z, w ∈ C we have sin( z + w ) = sin z cos w + cos z sin w . (c) Solve e z = 1 + i √ 3 for z ∈ C . (d) Solve sin z = i for z ∈ C ....
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 Fall '08
 ANDREWCHILDS
 Algebra, Equations, Complex Numbers, Complex number, cos z sin, sin z cos

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