How do you divide $\frac{6 i + 5}{7 i - 4}$ $( 6i+5) / ( 7 i -4 )$ in trigonometric form?

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Answer 1 · 2018-02-14T13:10:31

In trigonometric form: $0.969 (cos 1.214 - i sin 1.214)$ $0.969(cos 1.214-isin 1.214)$

$\frac{5 + 6 i}{- 4 + 7 i}$ $(5+6i)/(-4+7i)$ $Z = a + i b$ $Z=a+ib$ . Modulus: $| Z | = \sqrt{a^{2} + b^{2}}$ $|Z|=sqrt (a^2+b^2)$ ;

Argument: $θ = {tan}^{- 1} (\frac{b}{a})$ $theta=tan^-1(b/a)$ Trigonometrical form :

$Z = | Z | (cos θ + i sin θ); Z = 5 + 6 i$ $Z =|Z|(costheta+isintheta) ; Z= 5+6 i$ .

Modulus: $| Z | = \sqrt{5^{2} + 6^{2}} \approx 7.81$ $|Z|=sqrt(5^2+6^2)~~ 7.81$

Argument: $tan alpha= (|6|)/(|5|):. alpha = tan^-1 (1.2)=0.876$

$Z_1$ lies on first quadrant, so $theta =alpha ~~ 0.876$

$:. Z_1=7.81(cos 0.876+isin 0.876)$

$Z_2= -4 + 7i$ . Modulus: $|Z|=sqrt(4^2+7^2)$

$=sqrt 65 ~~ 8.062$ Argument: $tan alpha= (|7|)/(|-4|)$

$=7/4 :.alpha =tan^-1 (7/4) = 1.052 ; Z_2$ lies on second

quadrant. $:. theta=pi-alpha ~~2.09$

$:. Z_2=8.062(cos 2.09+isin 2.09) :. (5+6i)/(-4+7i) =$

$Z= (7.81(cos0.876+isin 0.876))/(8.062(cos 2.09+isin 2.09)$

$Z=0.969(cos(0.876-2.09)+isin (0.876-2.09))$ or

$Z=0.0969(cos 1.214-isin 1.214) =22/65-59/65i$

In trigonometric form: $0.969(cos 1.214-isin 1.214)$ [Ans]

How do you divide ( 6i+5) / ( 7 i -4 )6i+57i−4( 6i+5) / ( 7 i -4 ) in trigonometric form?