How do you write the complex number in trigonometric form 6−7i?

1 Answer
Jim G.
Sep 3, 2017

√85(cos(0.862)−isin(0.862))

Explanation:

to convert from complex to trig. form

that is x+yi→r(cosθ+isinθ) using

∙xr=√x2+y2

∙xθ=tan−1(yx)x;−π<θ≤π

here x=6 and y=−7

⇒r=√62+(−7)2=√85

6−7i is in the fourth quadrant so we must ensure that θ
is in the fourth quadrant

⇒θ=tan−1(76)=0.862← related acute angle

⇒θ=−0.862← in fourth quadrant

⇒6−7i=√85(cos(−0.862)+isin(−0.862))

[cos(−0.862=cos(0.862);sin(−0.862)=−sin(0.862)]

⇒6−7i=√85(cos(0.862)−isin(0.862))

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