-2-2i

in polar form = 2.8 cis 2.35??

-3+4i polar form = 5 cis 2.2???

1 - sqaureroot(3i) polar form = 2 cis 1.04??

What is cis?

never mind I have the right answers.

polar form z = r (cos O + i sin O ) is also written in an abbreviated form
z = r cis O

cos + sin = cis

Валерий Валерий answered
5 years ago

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Explain Bot Explain Bot answered
7 months ago

Yes, you are correct. In polar form, a complex number is represented as z = r cis θ, where "r" represents the magnitude (or modulus) of the complex number and "θ" represents the argument (or angle) of the complex number. The cis notation is a shorthand way of expressing the cosine and sine terms in the form cos(θ) + i sin(θ).

To convert a complex number from rectangular form (a + bi) to polar form, you can use the following steps:

1. Find the magnitude (r):
- Calculate the square root of the sum of the squares of the real and imaginary parts: r = √(a^2 + b^2).

2. Find the argument (θ):
- If a ≠ 0, calculate θ using the arctan function: θ = arctan(b/a).
- If a = 0 and b > 0, set θ = π/2.
- If a = 0 and b < 0, set θ = -π/2.
- If a = 0 and b = 0, the complex number is at the origin and has no defined argument.

3. Express the polar form:
- Write the complex number in the form z = r cis θ.

So, for example:
-2 - 2i in polar form would be:
- r = √((-2)^2 + (-2)^2) = √(4 + 4) = 2√2 ≈ 2.83
- θ = arctan((-2)/(-2)) = arctan(1) = π/4 radians ≈ 0.785 radians
- Polar form: z = 2.83 cis 0.785

Regarding your question about cis, it is an abbreviation for the cosine and sine terms used in polar form. Instead of writing cos(θ) + i sin(θ) every time, the cis notation simplifies it by writing cis(θ). So, cis can be seen as a way of representing the cosine and sine functions in a more compact form.