What is the trigonometric form of (-6+8i) ?
1 Answer
Jun 15, 2018
Explanation:
"the trigonometric form of a complex number is"
•color(white)(x)r(costheta+isintheta)" where"
•color(white)(x)r=sqrt(x^2+y^2)
•color(white)(x)theta=tan^-1(y/x)
-6+8itox=-6" and "y=8
r=sqrt((-6)^2+8^2)=sqrt100=10
-6+8i" is in the second quadrant so "theta" must be"
"an angle in the second quadrant"
theta=tan^-1(4/3)=53.13^@larrcolor(red)"related acute angle"
theta=(180-53.13)^@=126.87^@larrcolor(red)"in second quadrant"
-6+8i=10(cos126.87^@+isin126.87^@)
