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

##### 1 Answer

Mar 4, 2017

#### Explanation:

To convert from

#color(blue)"standard to trigonometric form"#

#"that is "(x,y)tor(costheta+isintheta)#

#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))#