# How do you write the complex number in standard form #3/2(cos300+isin300)#?

I'll assume the trigonometric arguments are in degrees.

We're asked to find the standard form of

So we have

By signing up, you agree to our Terms of Service and Privacy Policy

To write the complex number ( \frac{3}{2} (\cos 300^\circ + i \sin 300^\circ) ) in standard form, you can use Euler's formula, which states that ( e^{i\theta} = \cos \theta + i \sin \theta ).

First, convert ( 300^\circ ) to radians by using the conversion factor ( \frac{\pi}{180} ) since ( 1^\circ = \frac{\pi}{180} ) radians.

( 300^\circ \times \frac{\pi}{180} = \frac{5\pi}{6} ) radians.

Now, substitute ( \frac{5\pi}{6} ) into Euler's formula:

( e^{i \frac{5\pi}{6}} = \cos \frac{5\pi}{6} + i \sin \frac{5\pi}{6} )

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

Now, multiply ( \frac{3}{2} ) by this result to get the complex number in standard form:

( \frac{3}{2} \times \left( -\frac{\sqrt{3}}{2} + i \left(-\frac{1}{2}\right) \right) )

( = -\frac{3\sqrt{3}}{4} - \frac{3i}{4} )

So, the complex number ( \frac{3}{2} (\cos 300^\circ + i \sin 300^\circ) ) in standard form is ( -\frac{3\sqrt{3}}{4} - \frac{3i}{4} ).

By signing up, you agree to our Terms of Service and Privacy Policy

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.

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.

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.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7