How do you write #2 +4i# in trigonometric form?

1 Answer
Jim G.
Apr 12, 2018

#2sqrt5(cos(1.107)+isin(1.107))#

Explanation:

#"to convert to trigonometric form"#

#"that is "x+yitor(costheta+isintheta)" using"#

#•color(white)(x)r=sqrt(x^2+y^2)#

#•color(white)(x)theta=tan^-1(y/x);-pi < theta <=pi#

#"here "x=2" and "y=4#

#rArrr=sqrt(2^2+4^2)=sqrt20=2sqrt5#

#theta=tan^-1(2)=1.107" radians to 3 dec. places"#

#rArr2+4i=2sqrt5(cos(1.107)+isin(1.107))#

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