SOLUTION: Write z1 and z2 in polar form. (Express &#952; in radians. Let 0 &#8804; &#952; < 2&#960;.) z1 = sqrt(3)+ i, z2 = 1 + sqrt(3i) Find z1z2 z1/z2 1/z1

Algebra ->  Trigonometry-basics -> SOLUTION: Write z1 and z2 in polar form. (Express &#952; in radians. Let 0 &#8804; &#952; < 2&#960;.) z1 = sqrt(3)+ i, z2 = 1 + sqrt(3i) Find z1z2 z1/z2 1/z1      Log On


   

Question 1131788: Write
z1 and z2 in polar form. (Express θ in radians. Let 0 ≤ θ < 2π.)
z1 = sqrt(3)+ i, z2 = 1 + sqrt(3i)
Find
z1z2
z1/z2
1/z1
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Write
z1 and z2 in polar form. (Express θ in radians. Let 0 ≤ θ < 2π.)
z1 = sqrt(3)+ i,
Note:: z1 is in QI
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r1 = sqrt((sqrt(3))^2+1^2) = 2
theta = arctan(1/sqrt(3)) = pi/6
So r1 = 2cis(pi/6)
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z2 = 1 + sqrt(3)i
r2 = 2
theta = arctan(sqrt(3)) = pi/3
So r2 = 2cis(pi/3)
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Find
z1z2 = r1*r2*cis(pi/6+2pi/6) = 4*cis(pi/2)
z1/z2 = r1/r2*cis(pi/6-2pi/6) = cis(-pi/6)
1/z1 = (1+ 0i)/((sqrt(3)+i) = cis(0)/[2*cis(pi/6)] = (1/2)cis(-pi/6)
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Cheers,
Stan H.
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