Given the complex number z_1=12(\cos\frac{13\pi}{8}+i\sin\frac{13\pi}{8})

chillywilly12a

chillywilly12a

Answered question

2021-09-18

Given the complex number z1=12(cos13π8+isin13π8) and z2=2(cos11π8+isin11π8), express the result of z1z2 in rectangular form with fully simplified fractions and radicals.

Answer & Explanation

grbavit

grbavit

Skilled2021-09-19Added 109 answers

Given two complex numbers, z1=12(cos(13π8)+isin(13π8))
and z2=2(cos(11π8)+isin(11π8))
We have to express z1z2 in rectangular form. Given complex numbers are of the form z=r(cos(θ)+isin(θ))
Changing z=r(cos(θ)+isin(θ)) to Euler form z=retθ we get,
z1=12e13x8 and z2=2e11x8
So, z=z1z2=12e13x82e11x8
=6e13x811x8
=6eπ4
=6(cos(π4)+isin(π4))
=6(22+i22)
=32(1+i)
z=32(1+i)

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