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[" Itlustration "3.21" If "z=re^(i theta...

[" Itlustration "3.21" If "z=re^(i theta)" ,then prove that "|e^(i-1)|=e^(-r sin theta)],[" Sol."quad z=re^(i theta)=r(cos theta+i sin theta)]

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If z=re^(i theta), then prove that |e^(iz)|=e^(-r sin theta)

z=i+sqrt(3)=r(cos theta+sin theta)

If z= re^(i theta)" then "|e^(iz)|=

" (i) "(cos theta+sin theta)/(cos theta-sin theta)

-1+i sqrt(3)=r e^(i theta) then theta=

"(cos theta+i sin theta)^(6)(cos theta-i sin theta)^(-3)

(cos theta + i sin theta) ^ (n) = cos n theta + i sin n theta

If z= re^(i theta ) , " then " |e^(iz) | is equal to a)1 b) e^(2r) sin theta c) e^( r sin theta) d) e^(-r sin theta)

If z=re^(i)theta then |e^(iz)| is equal to: