## Polar Form

Convert the following into polar form:

##
__
__**Hint**

**Hint**

Complex numbers can be written in both rectangular and polar form. For rectangular form, a complex number is represented by both its real and imaginary components:

$$$z=a+jb$$$

where
$$a$$
is the real component,
$$b$$
is the imaginary component, and
$$j=\sqrt{-1}$$
which is often expressed as
$$i=\sqrt{-1}$$
.

##
__
__**Hint 2**

**Hint 2**

Polar form is

$$$z=c\: \angle \: \theta $$$

where
$$c=\sqrt{a^2+b^2}$$
(the vector’s length) and
$$\theta=tan^{-1}(b/a)$$
. Note:
$$a=c\:cos(\theta)$$
and
$$b=c\:sin(\theta)$$
.

Complex numbers can be written in both rectangular and polar form. For rectangular form, a complex number is represented by both its real and imaginary components:

$$$z=a+jb$$$

where
$$a$$
is the real component,
$$b$$
is the imaginary component, and
$$j=\sqrt{-1}$$
which is often expressed as
$$i=\sqrt{-1}$$
.

Thus, our rectangular coordinate form can be rewritten as:

$$$7+\sqrt{-1}\sqrt{16}\to 7+4i$$$

where
$$a=7$$
and
$$b=4$$
.

Polar form is:

$$$z=c\: \angle \: \theta $$$

where
$$c=\sqrt{a^2+b^2}$$
(the vector’s length) and
$$\theta=tan^{-1}(b/a)$$
. Note:
$$a=c\:cos(\theta)$$
and
$$b=c\:sin(\theta)$$

Therefore,

$$$c=\sqrt{7^2+4^2}=\sqrt{49+16}=\sqrt{65}=8.06$$$

$$$\theta=tan^{-1}(\frac{4}{7})=29.7^{\circ}$$$

Finally, the polar form is:

$$$8.06 \: \angle \: 29.7^{\circ}$$$

$$$8.06 \: \angle \: 29.7^{\circ}$$$