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

Question

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

jgardner33v4 · Accepted Answer

(13−i)4(13−i)2(13−i)2&amp;nbsp;Now&amp;nbsp;(A−B)2=A2+B2−2AB&amp;nbsp;(13+i2−213i)(13+i2−213i)&amp;nbsp;i2=−1&amp;nbsp;(12−213i)(12−213i)&amp;nbsp;(144+4×13i−2−413i)&amp;nbsp;(144−52−413i)&amp;nbsp;=92−413i→&amp;nbsp;rectangular form&amp;nbsp;r=(92)2+(413)2&amp;nbsp;r=8464+208⇒r8672&amp;nbsp;r=4542&amp;nbsp;θ=tan4(−41392)&amp;nbsp;θ=tan−1(−1323)&amp;nbsp;=reiθ⇒4542eitan−1(−1323)

reinosodairyshm · Accepted Answer

Say&amp;nbsp;(13−i)4&amp;nbsp;⇒((13−1)2)2&amp;nbsp;⇒((13)2+(i)2−2⋅13.i)2&amp;nbsp;⇒(13+(−1)−213i)2&amp;nbsp;⇒(12−213i)2&amp;nbsp;⇒(12)2+(213i)2−2⋅12⋅213i&amp;nbsp;⇒144+52i2−4813i&amp;nbsp;⇒144−52−4813i&amp;nbsp;⇒92+(−4813i)&amp;nbsp;This is in the form of&amp;nbsp;x+iy,&amp;nbsp;x=92,y=(−4813)&amp;nbsp;if&amp;nbsp;reiθ&amp;nbsp;v=(92)2+(−4813)2&amp;nbsp;=x2+yn&amp;nbsp;⇒r=38,416&amp;nbsp;⇒r=196.&amp;nbsp;⇒θ=(360∘−61.99∘)&amp;nbsp;⇒θ=298.01∘&amp;nbsp;⇒θ≈298∘=7745&amp;nbsp;=reiθ=196ei⋅298∘=196⋅ei7745&amp;nbsp;(answer)

alenahelenash · Accepted Answer

(13−i)2(13−i)2 Now (A−B)2=A2+B2−2AB (13+i2−213i)(13+i2−213i) i2=−1 (12−213i)(12−213i) (144+4×13i−2−413i) (144−52−413i) =92−413i→ rectangular form Now r=(92)2+(413)2 r=8464+208⇒r8672 r=4542 θ=tan4⁡(−41392) θ=tan−1⁡(−1323) Answer: =reiθ⇒4542eitan−1⁡(−1323)

Write the expression in rectangular form, x+yi, and in exponential form re^{i \theta}. N

Answered question

Answer & Explanation

New Questions in Pre-Algebra