Precalculus, Chapter 6, 6.5, Section 6.5, Problem 19

-7+4i
The trigonometric form of a complex number z=x+yi is:
z=r(cos theta + i sintheta)
where
r=sqrt(x^2+y^2)
and
theta= tan^(-1)y/x
Applying these formulas, the values of r and theta pf x=-7+4i are:
r=sqrt((-7)^2+4^2)=sqrt(49+16)=sqrt65
theta=tan^(-1) (-7)/4=-29.744813^o
Since x is negative and y is positive, the angle is located at the second quadrant. The equivalent positive angle of theta is:
theta =180^o +(-29.744813^o)=150.2551870^o
Rounding off to two decimal places, it becomes:
theta=150.26^o
Plugging the values of r and theta to the trigonometric form yields:
z=sqrt65(cos 150.26^o + isin 150.26^o)

Therefore, the trigonometric form of -7+4i is sqrt65(cos 150.26^o + isin150.26^o) .