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Assume that x, y E R and z = x + iy E C and answer the followings: 1. Evaluate exp() =? – exp("",) =? 2

Assume that x, y E R and z = x + iy E C and answer the followings: 1. Evaluate exp() =? – exp("",) =? 2

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 18E
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Assume that x, y E R and z = x + iy E C and answer the followings: 

Assume that x,y ER and z = x + iy E C and answer the followings: 1. Evaluate exp(G =? TT (i-2 exp( =? 2 (πί 2. Evaluate all values of Log ,Log (-2), 2', 271/3,i2, i!/3, (8/Zi + 8VZ)", (i')', ¿«">
Transcribed Image Text:Assume that x,y ER and z = x + iy E C and answer the followings: 1. Evaluate exp(G =? TT (i-2 exp( =? 2 (πί 2. Evaluate all values of Log ,Log (-2), 2', 271/3,i2, i!/3, (8/Zi + 8VZ)", (i')', ¿«">
Expert Solution
Step 1

Note: As per bartleby instruction when more than one question is given only one has to be answered. Please upload other separately

Given that z=x+iy

(1) eπi2

It is known that eix=cosx+isinx

So,

eπi2=cosπ2+isinπ2=0+i=i

Since cosπ2=0, sinπ2=1

So z=i⇒x=0,y=1.

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