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10:19 quiz04.pdf Basie Physies PHY 114-W-0 Medgar Even Quie 3
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(1)Product=(3i+4j)(i-5j)=((3).(1))i+((4)(-5))j=3i-20j

rectangular: form=3i-20j

(2) (a)Given (r,θ), (x,y) can be found by doing (r cosθ,r sinθ)

r=8, heta=rac{pi}{4}

(z, y) . (Scos(4), 8sin(4) ะ (7.99. 0.11)

Rectangular form = 7.99i+0.11)

(b)

r=1, heta=pi

(т, y) → (1cos(n), îsin(n)) ะ (0.99.0054)

Rectangular form= 0.99i+ 0.054 j)

(4) a)2j

(z, y) = (0.2)

r=sqrt{x^{2}+y^{2}}=sqrt{0^{2}+2^{2}}=2

heta=arctan (rac{y}{x})=arctan (rac{2}{0})=90^{o}

Polar: form=(r, heta)=(2,90^{o})

(b)5i+5j

(x,y)=(5,5)

r=sqrt{x^{2}+y^{2}}=sqrt{5^{2}+5^{2}}=7.07

θ arctan

Polar: form=(r, heta)=(7.07,45^{o})

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