How do you simplify #4(cos((9pi)/4)+ising((9pi)/4))div2[cos(-pi/2)+isin(-pi/2)]# and express the result in rectangular form?

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How do you simplify #4(cos((9pi)/4)+isin((9pi)/4))div2[cos(-pi/2)+isin(-pi/2)]# and express the result in rectangular form?

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Answer 1 · 2017-03-24T13:02:21

#-sqrt2(1-i).#

Recall that, #r(costheta+isintheta)# is also denoted, as #rcistheta,# &,

#r_1cisalpha-:r_2cisbeta=(r_1/r_2)cis(alpha-beta)#.

Using these, we find, that,

#"The given Exp.="4cis(9pi/4)div2cis(-pi/2)#

#=(4/2)[cis{(9pi/4)-(-pi/2)}].#

#=2{cis(9pi/4+pi/2)}.#

#=2cis(11pi/4).#

#=2{cos(11pi/4)+isin(11pi/4)}.#

#=2{cos(3pi-pi/4)+isin(3pi-pi/4)}.#

#=2{-cos(pi/4)+isin(pi/4)}.#

#=2(-1/sqrt2+i1/sqrt2).#

#:." The Exp.="-sqrt2(1-i).#

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