How do you write #2(cos300+isin300) in retangular form?

Answer 1

The answer is: #z=1-sqrt3i#.

An example of a complex number's rectangular form is:

#z=a+ib#,

and we have the following number expressed in trigonometric form:

#z=rho(sintheta+icostheta)#.

So the real part of the numer is #rhosintheta=2cos300°=2*1/2=1# and the imaginary part is #2sin300°=2*(-sqrt3/2)=-sqrt3#.

So:

#z=1-sqrt3i#.

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Answer 2

James Adkins

To write (2(\cos 300^\circ + i\sin 300^\circ)) in rectangular form, we use Euler's formula, which states that (e^{i\theta} = \cos \theta + i \sin \theta). Thus, we have:

[2(\cos 300^\circ + i\sin 300^\circ) = 2(e^{i\cdot300^\circ})]

Now, using Euler's formula:

[2(e^{i\cdot300^\circ}) = 2(\cos(300^\circ) + i\sin(300^\circ))]

[= 2\left(\frac{1}{2} - i\frac{\sqrt{3}}{2}\right)]

[= 1 - i\sqrt{3}]

So, (2(\cos 300^\circ + i\sin 300^\circ)) in rectangular form is (1 - i\sqrt{3}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.