Write the expression in rectangular form, x+yi, and in exponential form reiθ. (13−i)4 The rectangular...

kramtus51

kramtus51

Answered

2022-01-18

Write the expression in rectangular form, x+yi, and in exponential form reiθ.
(13i)4
The rectangular form of the given expression is ?, and the exponential form of the given expression is ? (Simplify your answers. Use integers or decimals for any numbers in the expressions. Round the final answer to three decimal places as needed intermediate values to four decimal places as needed.)

Answer & Explanation

jgardner33v4

jgardner33v4

Expert

2022-01-19Added 35 answers

(13i)4
(13i)2(13i)2 
Now (AB)2=A2+B22AB 
(13+i2213i)(13+i2213i) 
i2=1 
(12213i)(12213i) 
(144+4×13i2413i) 
(14452413i) =92413i rectangular form 
r=(92)2+(413)2 
r=8464+208r8672 
r=4542 
θ=tan4(41392) 
θ=tan1(1323) =reiθ4542eitan1(1323)

reinosodairyshm

reinosodairyshm

Expert

2022-01-20Added 36 answers

Say (13i)4 
((131)2)2 
((13)2+(i)2213.i)2 
(13+(1)213i)2 
(12213i)2 
(12)2+(213i)2212213i 
144+52i24813i 
144524813i 
92+(4813i) 
This is in the form of x+iyx=92,y=(4813) 
if reiθ 
v=(92)2+(4813)2 
=x2+yn 
r=38,416 
r=196
θ=(36061.99) 
θ=298.01 
θ298=7745 =reiθ=196ei298=196ei7745 (answer)

alenahelenash

alenahelenash

Expert

2022-01-24Added 366 answers

(13i)2(13i)2 Now (AB)2=A2+B22AB (13+i2213i)(13+i2213i) i2=1 (12213i)(12213i) (144+4×13i2413i) (14452413i) =92413i rectangular form Now r=(92)2+(413)2 r=8464+208r8672 r=4542 θ=tan4(41392) θ=tan1(1323) Answer: =reiθ4542eitan1(1323)

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