Find the produce for z1 and z2 please show your work Find th

Find the produce for z1 and z2
please show your work!

Find the product for z_1 = squareroot(3)[cos (5 phi/4) + i sin (5 phi/4)] and z_2 = 2[cos(n) + i sin(n)] Find the produce for z1 and z2

Solution

z1 = sqrt3[ cos5pi/4 +jsinsinpi/4 ]

z2 = 2[cospi + jsinpi ]

In polar form z1 = sqrt(3)e^(j5pi/4)

In polar form z2 = 2e^(jpi)

Now Z = z1*z2 = 2sqrt3e^i(5pi/4+pi)

= 2sqrt(3)e^j(5pi/4 +pi)

2sqrt(3)[ cos(5pi/4 +pi) +j sin(5pi/4+pi) ]

= 2sqrt(3)[ 1/sqrt2 +j1/sqrt2]

= sqrt6 + jsqrt6