How do you divide $( -i+4) / (7i +5 )$ in trigonometric form?

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Answer 1 · 2016-01-27T08:09:43

$sqrt1258/74*[cos (tan^-1 ((-33)/13))+isin (tan^-1 ((-33)/13))]$ OR

$sqrt1258/74*[cos(-68.4986^@)+isin(-68.4986^@)]$

$(-i+4)/(7i+5)=(4-i)/(5+7i)$

$(4-i)/(5+7i)*(5-7i)/(5-7i)=(20-5i-28i-7)/(25+49)=(13-33i)/74$

$13/74-33/74i$

Compute the magnitude $r$ ,let $x=13/74$ and $y=(-33)/74$

$r=sqrt(x^2+y^2)=sqrt((13/74)^2+((-33)/74)^2)=sqrt1258/74$

Compute the Argument $phi$

$phi=tan^-1 (y/x)=tan^-1 (((-33)/cancel74)/(13/cancel74))=tan^-1 ((-33)/13)$

$phi=-68.4986^@$

so that

$(-i+4)/(7i+5)=(4-i)/(5+7i)$

$(4-i)/(5+7i)=sqrt1258/74*[cos(-68.4986^@)+isin(-68.4986^@)]$

How do you divide ( -i+4) / (7i +5 )( -i+4) / (7i +5 ) in trigonometric form?