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Answer:
a)z1.z2=cos (5pi/2) + i sin(5pi/2)
b)z1.z2=6[cos 80 + isin 80]
c)z1/z2= 3[cos 3pi + i sin 3pi]
d)z1/z2 = (cos 7pi/12 + i sin 7pi/12 )
Step-by-step explanation:
a) z1=2(cos pi/6 + i sinpi/6) , z2=3(cospi/4 + i sin pi/4)
z1.z2=[2(cos pi/6 +i sinpi/6)] . [3(cospi/4 + i sin pi/4)]
z1.z2=6[cos(pi/6 + pi/4) + i sin(pi/6 + pi/4)]
z1.z2=6[cos (5pi/12) + i sin(5pi/12)]
z1.z2=cos (5pi/2) + i sin(5pi/2)
Hence the answer is this.
b)z1= 2/3 (cos60° + i sin60°) , z2=9 (cos20° + i sin20°)
z1.z2=2/3 *9[(cos 60 +i sin60)+(cos20 + i sin20)]
z1.z2=18/3[cos(60+20) + i sin(60+20)]
z1.z2=6[cos 80 + isin 80]
Hence the answer is this
c) z1 = 12 (cos pi/3 -+i sin pi/3) , z2 = 3 (cos 5pi/6 + i sin 5pi/6)
z1/z2= (12/3)[(cos pi/3 + i sin pi/3) - (cos 5pi/6 + i sin 5pi/6)]
z1/z2= 6[cos(pi/3 - 5pi/6) + i sin(pi/3 - 5pi/6)]
z1/z2= 6[cos(2pi- pi/2) + i sin(2pi-pi/2)]
z1/z2= 6[cos 3pi/2 + i sin 3pi/2]
z1/z2= 3[cos 3pi + i sin 3pi]
Hence the answer is this
d) z1 = cos 2pi/3 + i sin 2pi/3 and z2 = 2 (cos pi/12 + i sin pi/12)
z1/z2 = (1/2)(cos(2pi/3-pi/12) + i sin (2pi/3 -pi/12))
z1/z2 = (cos 7pi/12 + i sin 7pi/12 )
Hence the answer is this