How do you divide $\frac{7 - 9 i}{- 2 - 9 i}$ $(7-9i)/(-2-9i)$ in trigonometric form?

Question

How do you divide $\frac{7 - 9 i}{- 2 - 9 i}$ $(7-9i)/(-2-9i)$ in trigonometric form?

1 Answer

Impact of this question

1817 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-21T04:50:34

$\frac{\sqrt{442}}{17} [cos ({tan}^{- 1} (\frac{- 81}{- 67})) + i \cdot sin ({tan}^{- 1} (\frac{- 81}{- 67}))]$ $sqrt(442)/17[cos(tan^-1((-81)/-67))+i*sin(tan^-1((-81)/-67))]$ OR

$\frac{\sqrt{442}}{17} [cos ({50.403791360249}^{\circ}) + i \cdot sin ({50.403791360249}^{\circ})]$ $sqrt(442)/17[cos(50.403791360249^@)+i*sin(50.403791360249^@)]$

Explanation:

Convert to Trigonometric forms first

$7 - 9 i = \sqrt{130} [cos ({tan}^{- 1} (\frac{- 9}{7})) + i sin ({tan}^{- 1} (\frac{- 9}{7}))]$ $7-9i=sqrt130[cos(tan^-1((-9)/7))+i sin(tan^-1((-9)/7))]$

$- 2 - 9 i = \sqrt{85} [cos ({tan}^{- 1} (\frac{- 9}{- 2})) + i sin ({tan}^{- 1} (\frac{- 9}{- 2}))]$ $-2-9i=sqrt85[cos(tan^-1((-9)/-2))+i sin(tan^-1((-9)/-2))]$

Divide equals by equals

$\frac{7 - 9 i}{- 2 - 9 i} =$ $(7-9i)/(-2-9i)=$

$(\frac{\sqrt{130}}{\sqrt{85}}) [cos ({tan}^{- 1} (\frac{- 9}{7}) - {tan}^{- 1} (\frac{- 9}{- 2})) + i sin ({tan}^{- 1} (\frac{- 9}{7}) - {tan}^{- 1} (\frac{- 9}{- 2}))]$ $(sqrt130/sqrt85)[cos(tan^-1((-9)/7)-tan^-1((-9)/-2))+i sin(tan^-1((-9)/7)-tan^-1((-9)/-2))]$

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

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

$\frac{\sqrt{442}}{17} [cos ({tan}^{- 1} (\frac{- 81}{- 67})) + i \cdot sin ({tan}^{- 1} (\frac{- 81}{- 67}))]$ $sqrt(442)/17[cos(tan^-1((-81)/-67))+i*sin(tan^-1((-81)/-67))]$

have a nice day!

Science

Math

Humanities

... and beyond

How do you divide $\frac{7 - 9 i}{- 2 - 9 i}$ $(7-9i)/(-2-9i)$ in trigonometric form?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you divide 7−9i−2−9i (7-9i)/(-2-9i) in trigonometric form?

1 Answer

Explanation:

Related questions

Impact of this question

How do you divide $\frac{7 - 9 i}{- 2 - 9 i}$ $(7-9i)/(-2-9i)$ in trigonometric form?