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

Answer:

Step-by-step 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=$8(cos40^{{\circ}}+isin40^{{\circ}}){\times}4(cos135^{{\circ}}+isin135^{{\circ}})$=$32(cos40^{{\circ}}cos135^{{\circ}}+isin40^{{\circ}}cos135^{{\circ}}+isin135^{{\circ}}cos40^{{\circ}}-sin40^{{\circ}}sin135^{{\circ})$

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

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