How do you write the complex number in trigonometric form $2 + 2 i$ $2+2i$ ?

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How do you write the complex number in trigonometric form $2 + 2 i$ $2+2i$ ?

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Answer 1 · 2017-06-15T12:30:21

$2 \sqrt{2} (cos (\frac{π}{4}) + i sin (\frac{π}{4}))$ $2sqrt2(cos(pi/4)+isin(pi/4))$

Explanation:

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

$that is x + y i \to r (cos θ + i sin θ) where$ $"that is " x+yitor(costheta+isintheta)" where "$

$∙ r = \sqrt{x^{2} + y^{2}}$ $• r=sqrt(x^2+y^2)$

$∙ θ = {tan}^{- 1} (\frac{y}{x})$ $• theta=tan^-1(y/x)$

$here x = 2 and y = 2$ $"here " x=2" and " y=2$

$\Rightarrow r = \sqrt{2^{2} + 2^{2}} = \sqrt{8} = 2 \sqrt{2}$ $rArrr=sqrt(2^2+2^2)=sqrt8=2sqrt2$

$θ = {tan}^{- 1} (\frac{2}{2}) = {tan}^{- 1} (1) = \frac{π}{4}$ $theta=tan^-1(2/2)=tan^-1(1)=pi/4$

$\Rightarrow 2 + 2 i = 2 \sqrt{2} (cos (\frac{π}{4}) + i sin (\frac{π}{4}))$ $rArr2+2i=2sqrt2(cos(pi/4)+isin(pi/4))$

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How do you write the complex number in trigonometric form $2 + 2 i$ $2+2i$ ?

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How do you write the complex number in trigonometric form 2+2i2+2i?

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How do you write the complex number in trigonometric form $2 + 2 i$ $2+2i$ ?