How do you divide $\frac{6 i - 3}{7 i - 4}$ $( 6i-3) / ( 7 i -4 )$ in trigonometric form?

Question

How do you divide $\frac{6 i - 3}{7 i - 4}$ $( 6i-3) / ( 7 i -4 )$ in trigonometric form?

1 Answer

Impact of this question

1394 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-21T07:28:28

$\frac{3 \sqrt{13}}{13} [cos ({tan}^{- 1} (\frac{- 1}{18})) + i \cdot sin ({tan}^{- 1} (\frac{- 1}{18}))]$ $(3sqrt(13))/13[cos(tan^-1((-1)/18))+i*sin(tan^-1((-1)/18))]$ OR

$\frac{3 \sqrt{13}}{13} [cos ({356.82016988014}^{\circ}) + i \cdot sin ({356.82016988014}^{\circ})]$ $(3sqrt(13))/13[cos(356.82016988014^@)+i*sin(356.82016988014^@)]" "$

Explanation:

Convert to Trigonometric forms first

$- 3 + 6 i = 3 \sqrt{5} [cos ({tan}^{- 1} (\frac{6}{- 3})) + i sin ({tan}^{- 1} (\frac{6}{- 3}))]$ $-3+6i=3sqrt5[cos(tan^-1((6)/(-3)))+i sin(tan^-1((6)/(-3)))]$

$- 4 + 7 i = \sqrt{65} [cos ({tan}^{- 1} (\frac{7}{- 4})) + i sin ({tan}^{- 1} (\frac{7}{- 4}))]$ $-4+7i=sqrt65[cos(tan^-1((7)/(-4)))+i sin(tan^-1((7)/(-4)))]$

Divide equals by equals

$\frac{- 3 + 6 i}{- 4 + 7 i} =$ $(-3+6i)/(-4+7i)=$

$(\frac{\sqrt{45}}{\sqrt{65}}) [cos ({tan}^{- 1} (\frac{6}{- 3}) - {tan}^{- 1} (\frac{7}{- 4})) + i sin ({tan}^{- 1} (\frac{6}{- 3}) - {tan}^{- 1} (\frac{7}{- 4}))]$ $(sqrt45/sqrt65)[cos(tan^-1((6)/(-3))-tan^-1((7)/(-4)))+i sin(tan^-1((6)/(-3))-tan^-1((7)/(-4)))]$

Take note of the formula:

$tan (A - B) = \frac{tan A - tan B}{1 + tan A \cdot tan B}$ $tan (A-B)=(Tan A-Tan B)/(1+Tan A* Tan B)$

also

$A - B = {tan}^{- 1} (\frac{tan A - tan B}{1 + tan A \cdot tan B})$ $A-B=Tan^-1 ((Tan A-Tan B)/(1+Tan A* Tan B))$

$\frac{3 \sqrt{13}}{13} [cos ({tan}^{- 1} (\frac{- 1}{18})) + i \cdot sin ({tan}^{- 1} (\frac{- 1}{18}))]$ $(3sqrt(13))/13[cos(tan^-1((-1)/18))+i*sin(tan^-1((-1)/18))]$

$\frac{3 \sqrt{13}}{13} [cos (6.2276868019339) + i \cdot sin (6.2276868019339)]$ $(3sqrt(13))/13[cos(6.2276868019339)+i*sin(6.2276868019339)]" "$ radian angles

$\frac{3 \sqrt{13}}{13} [cos ({356.82016988014}^{\circ}) + i \cdot sin ({356.82016988014}^{\circ})]$ $(3sqrt(13))/13[cos(356.82016988014^@)+i*sin(356.82016988014^@)]" "$

Science

Math

Humanities

... and beyond

How do you divide $\frac{6 i - 3}{7 i - 4}$ $( 6i-3) / ( 7 i -4 )$ in trigonometric form?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you divide 6i−37i−4( 6i-3) / ( 7 i -4 ) in trigonometric form?

1 Answer

Explanation:

Related questions

Impact of this question

How do you divide $\frac{6 i - 3}{7 i - 4}$ $( 6i-3) / ( 7 i -4 )$ in trigonometric form?