Question

Whatis the tigonemtric form of -3+4i

Answer 1

We calculate the module:

$|z|\: = \: \sqrt{( - 3) ^{2} \: + \: {4}^{2} }$

$|z| \: = \: \sqrt{9 \: + \: 16}$

$|z| \: = \: \sqrt{25}$

$\boxed{|z| \: = \: 5}$

We calculate the angle formed by "z":

$\arctan( \frac{4}{ - 3} ) \: = \: \underline{0.92729521 \: \text{rad}}$

We pass it to degrees:

$0.92729521 \: \times \: \frac{180}{\pi}$

$\frac{166.91313924}{\pi}$

$\frac{166.91313924}{3.14159265}$

$\boxed{ 53.13°}$

Now we use this formula to transform it into a trigonometric form:

$\boxed{z \: = \: |z| \times \: ( \cos( \alpha) \: + \: i \: \times \: \sin( \alpha))}$

We substitute the values already obtained:

$\boxed{ \bold{z \: = \: 5 \times \: ( \cos( 53.13°) \: + \: i \: \times \: \sin( 53.13°))}}$

Answer:

$\boxed{ \bold{z \: = \: 5 \times \: ( \cos( 53.13°) \: + \: i \: \times \: \sin( 53.13°))}}$

MissSpanish