Question 935628
Use the FOIL method,
{{{(3+2j)(1+7j)=3+21j+2j+14j^2}}}
{{{(3+2j)(1+7j)=(3-14)+23j}}}
{{{(3+2j)(1+7j)=-11+23j}}}
.
.
.
{{{(3+2j)(1+7j)=((3+2j)/(1+7j))((1-7j)/(1-7j))}}}
{{{(3+2j)(1+7j)=((3+2j)(1-7j))/((1+7j)(1-7j))}}}
{{{(3+2j)(1+7j)=(3-21j+2j-14j^2)/(1-7j+7j-49j^2)}}}
{{{(3+2j)(1+7j)=(17-19j)/(50)}}}
.
.
.
{{{Z[1]}}}
{{{R[1]=sqrt(3^2+2^2)=sqrt(13)}}}
{{{alpha=tan^(-1)(2/3)=33.7}}}
.
.
{{{Z[2]}}}
{{{R[2]=sqrt(1^2+7^2)=sqrt(50)=5sqrt(2)}}}
{{{beta=tan^(-1)(7/1)=81.9}}}
.
.
{{{Z[1]*Z[2]=sqrt(13)*5sqrt(2)*(cos(33.7+81.9)+i*sin(33.7+81.9))}}}
{{{Z[1]*Z[2]=5sqrt(26)*(cos(115.6)+i*sin(115.6))}}}
.
.
{{{Z[1]/Z[2]=sqrt(13)/(5sqrt(2))*(cos(33.7-81.9)+i*sin(33.7-81.9))}}}
{{{Z[1]/Z[2]=(sqrt(26)/10)*(cos(-48.2)+i*sin(-48.2))}}}
{{{Z[1]/Z[2]=(sqrt(26)/10)*(cos(311.8)+i*sin(311.8))}}}