`-7 + 4i` Write the trigonometric form of the number.

`-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)` .