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Unformatted text preview: , 0) or what is the same 1+0 i . In the same way, translating two units down corresponds to adding2 i . Now, rotation corresponds to multiplication, in this case, by e i 6 . Therefore we need to compute ((1 + i ) + 1 + (2 i )) e i 6 . This multiplication is easier to perform in binomial form. We have that e i 6 = cos 6 + i sin 6 = 3 2 + i 1 2 and therefore we need to multiply (2i )( 3 2 + i 1 2 ) = ( 3 2 +1)+ i (1 3 2 ). (Notice that we get the exact answer explicitly. The computation in polar form is less convenient in this case to do the multiplication.) 5. Compute 3 1 + i Solution: 3 1 + i = 3 p 2 e i 4 = 2 1 / 6 e i / 4+2 k 3 for k = , 1 , 2....
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 Spring '09

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