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Let z1 = 4(cos 135° + i sin 135°) and z2 = 2(cos 45° + i sin 45°). Write the rectangular form of z1z2.?

+1 vote
Let z1 = 4(cos 135° + i sin 135°) and z2 = 2(cos 45° + i sin 45°). Write the rectangular form of z1z2.

Can someone help me ? Explain
asked Mar 6, 2013 in TRIGONOMETRY by anonymous Apprentice

1 Answer

+1 vote

135 degrees = 3pi / 4
45 degrees = pi/4

cos(t) + i * sin(t) = e^(t * i)

z1 = 4 * e^((3pi/4) * i)
z2 = 2 * e^((pi/4) * i)

Now we just use the rules of exponents and expand

z1 * z2 =>
4 * 2 * e^((3pi/4) * i + (pi/4) * i) =>
8 * e^(pi * i) =>
8 * (cos(pi) + i * sin(pi)) =>
8 * (-1 + i * 0) =>
8 * (-1 + 0) =>
8 * (-1) =>
-8

answered Mar 6, 2013 by kevin Rookie
z1/z2=4 * e^((3pi/4) * i)/2 * e^((pi/4) * i)
         =2*e^((3pi/4-pi/4)i
         =2e(pi/2)i
         =2(cospi/2+isinpi/2)
         =2i

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