Find z1z2 and z1 lz2 for the following pair of complex numbe

Find z_1z_2 and z_1 lz_2 for the following pair of complex numbers, using trigonometric form. z_1 = squareroot 3 + i, z_2 = 5 + 5 i squareroot 3 z_1z_2 = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Type your answer in the form a + b i.) z_1lz_2 = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Type your answer in the form a + b i.)

Solution

z₁=3 +i ,z₂=5+ 5i3

z₁=2*((3_/2) +i(1_/2)) ,z₂=5*(1+ i3)

z₁=2*((3_/2) +i(1_/2)) ,z₂=10*((1_/2)+ i(3_/2))

z₁=2*(cos30^o +i sin30^o) ,z₂=10*(cos60^o +i sin60^o)

z₁z₂=2*(cos30^o +i sin30^o) *10*(cos60^o +i sin60^o)

z₁z₂=20*(cos(30+60)^o +i sin(30+60)^o)

z₁z₂=20*(cos(90)^o +i sin(90)^o)

z₁z₂=20*(0 +i*1)

z₁z₂=20i

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z₁/z₂=2*(cos30^o +i sin30^o)_{/10*(cos60^o +i sin60^o)}

z₁/z₂=(2_/10)*(cos(30-60)^o +i sin(30-60)^o)

z₁/z₂=(2_/10)*(cos(-30)^o +i sin(-30)^o)

z₁/z₂=(2_/10)*((3_/2) -i(1_/2))

z₁/z₂=((3_/10) -i(1_/10))