How do you find the trigonometric form of $- 7 + 7 i$ $-7+7i$ ?

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Answer 1 · 2018-07-16T05:19:39

The trigonometric form is $z = 7 \sqrt{2} (cos (\frac{3}{4} π) + i sin (\frac{3}{4} π))$ $z=7sqrt2(cos(3/4pi)+isin(3/4pi))$ , $[mod 2pi]$

To convert a complex number

$z=x+iy$

to the polar form

$z=r(costheta+isintheta)$

Apply the following :

${(r=|z|=sqrt(x^2+y^2)),(costheta=x/(|z|)),(sintheta=y/(|z|)):}$

Here,

$z=-7+7i$

$|z|=sqrt((-7)^2+(7)^2)=sqrt(49+49)=sqrt98=7sqrt2$

Therefore,

$z=7sqrt2(-1/sqrt2+i/sqrt2)$

$=>$ , ${(costheta=-1/sqrt2),(sintheta=1/sqrt2):}$

$=>$ , $theta=3/4pi$

The trigonometric form is

$z=7sqrt2(cos(3/4pi)+isin(3/4pi))$ , $[mod 2pi]$

How do you find the trigonometric form of -7+7i−7+7i-7+7i?