What is the trigonometric form of (-7+2i) (−7+2i)?

1 Answer
Jim G.
Mar 4, 2017

sqrt53(cos(2.86)+isin(2.86))√53(cos(2.86)+isin(2.86))

Explanation:

To convert from color(blue)"standard to trigonometric form"standard to trigonometric form

"that is "(x,y)tor(costheta+isintheta)that is (x,y)→r(cosθ+isinθ)

color(red)(bar(ul(|color(white)(2/2)color(black)(r=sqrt(x^2+y^2))color(white)(2/2)|)))

"and " color(red)(bar(ul(|color(white)(2/2)color(black)(theta=tan^-1(y/x))color(white)(2/2)|)))
color(white)(xxxx)"where" -pi < theta<=pi

"here " x=-7" and "y=2

rArrr=sqrt((-7)^2+2^2)=sqrt53

"Since "-7+2i is in the second quadrant, we must ensure that theta is in the second quadrant.

theta=pi-tan^-1(2/7)

rArrtheta=(pi-0.278)=2.86larr" in second quadrant"

rArr-7+2itosqrt53(cos(2.86)+isin(2.86))

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