Can you find the product of z1 and z2? z1=4(cos40˚+ i sin40˚) z2=2(cos20˚+ i sin20˚) Give your answer in rectangular form.

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Answer 1 · 2018-05-30T07:42:08

#z_1z_2=4+4sqrt3i#

there are two ways of doing this

method 1

#z_1=r_1(costheta+isintheta)#

#z_2=r_2(cosphi+isinphi)#

#=>z_1z_2=r_1r_2(cos(theta+phi)+isin(theta+phi))--(1)#

we have

#z_1=4(cos40+isin40)#

#z_2=2(cos20+isin20)#

#:.z_1z_2=(4xx2)(cos(40+20)+isin(40+20))#

#z_1z_2=8(cos60+isin60)#

#z_1z_2=8(1/2+isqrt3/2)#

#z_1z_2=4+4sqrt3i#

method 2

change

#z=r(costheta+isintheta)#

to Euler form

#z=re^(itheta)#

we have

#z_1z_2=r_1r_2e^(itheta)e^(iphi)#

#z_1z_2=r_1r_2e^(i(theta+phi))#

which gives us #(1)#

and continue from there as above