Polar
Convert the following into polar form:
Expand 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
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, the rectangular coordinate form can be rewritten as:
$$$5+\sqrt{-1}\sqrt{9}\to 5+3i$$$
where
$$a=5$$
and
$$b=3$$
.
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,
$$$c=\sqrt{5^2+3^2}=\sqrt{25+9}=\sqrt{34}=5.83$$$
$$$\theta=tan^{-1}(\frac{3}{5})=30.96^{\circ}$$$
Finally, the polar form is:
$$$5.83 \: \angle \: 30.96^{\circ}$$$
$$$5.83 \: \angle \: 30.96^{\circ}$$$
Time Analysis
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Similar Problems from FE Section: Algebra of Complex Numbers
344. Polar Form
345. Binomial Product
611. The Polar Form
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