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^@)#
