Question

Find the product of z1 and z2, where z1 = 8(cos 40° + i sin 40°) and z2 = 4(cos 135° + i sin 135°).

Answer 1

hello :
z1 × z2 = 32(cos(40° + 135°) + i sin ( 40° + 135°)
z1 × z2 = 32 (cos(175°) +i sin (175°)

Answer 2

Explanation:

The given equations are:

`z_(1)=8(cos40^{{\circ}}+isin40^{{\circ}})` and

`z_(2)=4(cos135^{{\circ}}+isin135^{{\circ}})`

The product of
`z_(1)` and
`z_(2)` is=
`8(cos40^{{\circ}}+isin40^{{\circ}}){*}4(cos135^{{\circ}}+isin135^{{\circ}})`=
`32(cos40^{{\circ}}cos135^{{\circ}}+isin40^{{\circ}}cos135^{{\circ}}+isin135^{{\circ}}cos40^{{\circ}}-sin40^{{\circ}}sin135^{{\circ})`

=
`32(cos(40+135)+isin(40+135))`

=
`32(cos175^{{\circ}}+isin175^{{\circ}})` whih is the required product.