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Ignore what I have written because I'm pretty sure its wrong. Thanks! Deliver the assignment to
my office, 4502 French Hal! West or Scan your assignment and send it as an email attachment.
Write the complex number, z = a + bi, in polar form, z = r (cos theta + i sin theta), with argument
theta between 0 and 2 pi. -3i 3 - Squareroot 3i -1 + i II. Find the product, z_1z_2, and the
quotient, z_1/z_2. Express your answer in polar form. z_1 = 3(cos 15 degree + i sin 15 degree)
z_2 = 6(cos 20 degree + i sin 20 degree) z_1z_2: ____ z_1/z_2: ____ z_1 = 21 (cso pi/5 + i sin
pi/5) z_2 = 7(cos 2 pi/3 + i sin 2 pi/3) z_1z_2: ____ z_1/z_2: ____
Solution
I)
1)
-3i
r=[02+(-3)2]=3
=tan-1(-3/0) =3/2
polar form is 3(cos(3/2)+i sin(3/2))
2)
3-3i
r=[32+(-3)2]=12=23
=tan-1(-3/3) =11/6
polar form is 23(cos(11/6)+i sin(11/6))
3)
-1+i
r=[(-1)2+12]=2
=tan-1(1/-1) =3/4
polar form is 2(cos(3/4)+i sin(3/4))
===========================================================
II)
1)
z1=3(cos15o+isin15o), z2=6(cos20o+isin20o)
z1z2=3(cos15o+isin15o)*6(cos20o+isin20o)
z1z2=3*6(cos(15+20)o+isin(15+20)o)
z1z2=18(cos(35)o+isin(35)o)
z1/z2=3(cos15o+isin15o)/[6(cos20o+isin20o)]
z1/z2=(3/6)(cos(15-20)o+isin(15-20)o)
z1/z2=(1/2)(cos(-5)o+isin(-5)o)
z1/z2=(1/2)(cos(355)o+isin(355)o)
2)
z1=21(cos(/5)+isin(/5)), z2=7(cos(2/3)+isin(2/3))
z1z2=21(cos(/5)+isin(/5))*7(cos(2/3)+isin(2/3))
z1z2=21*7(cos((/5)+(2/3))+isin((/5)+(2/3)))
z1z2=147(cos(13/15)+isin(13/15))
z1/z2=21(cos(/5)+isin(/5))/7(cos(2/3)+isin(2/3))
z1/z2=3(cos((/5)-(2/3))+isin((/5)-(2/3)))
z1/z2=3(cos(-7/15)+isin(-7/15))
z1/z2=3(cos(23/15)+isin(23/15))

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Ignore what I have written because Im pretty sure its wrong. Thank.pdf