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

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Answer 1 · 2018-02-27T12:08:15

In trigonometric form: $0.725 (cos 0.091 - i sin 0.091)$ $0.725(cos 0.091-isin 0.091)$

$\frac{4 + 4 i}{5 + 6 i}; Z = a + i b$ $(4+4i)/(5+6i) ;Z=a+ib$ . 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 :

$Z = | Z | (cos θ + i sin θ)$ $Z =|Z|(costheta+isintheta)$ $Z_{1} = 4 + 4 i$ $Z_1= 4+4 i$

Modulus: $| Z_{1} | = \sqrt{4^{2} + 4^{2}} \approx 5.66$ $|Z_1|=sqrt(4^2+4^2)~~ 5.66$

Argument: $tan alpha= (|4|)/(|4|):. alpha = tan^-1 (1)=0.785$

$Z_1$ lies on first quadrant, so $theta =alpha ~~ 0.785$

$:. Z_1=5.66(cos 0.785+isin 0.785)$

$Z_2= 5 + 6i$ . Modulus: $|Z|=sqrt(5^2+6^2)$

$=sqrt 61 ~~ 7.81$ Argument: $tan alpha= (|6|)/(|5|)$

$=6/5 :.alpha =tan^-1 (1.2) ~~ 0.0876 ; Z_2$ lies on first

quadrant. $:. theta=alpha ~~0.876$

$:. Z_2=7.81(cos 0.876+isin 0.876) :. (4+4i)/(5+6i) =$

$Z= (5.66(cos0.785+isin 0.785))/(7.81(cos 0.876+isin 0.876)$

$Z=0.725(cos(0.785-0.876)+isin (0.785-0.876))$ or

$Z=0.725(cos (-0.091)+isin (-0.091))$ or

$Z=0.725(cos (0.091)-isin (0.091))=(44/61-4/61 i )$

In trigonometric form: $0.725(cos 0.091-isin 0.091)$ [Ans]

How do you divide ( 4i+4) / (6i +5 )4i+46i+5( 4i+4) / (6i +5 ) in trigonometric form?