Polar Form Calculator

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Example

Created on 2024-06-20Asked by Mason Clark (Solvelet student)

Express the complex number

z = 3 + 4i

in polar form.

Solution

To express the complex number

z = 3 + 4i

in polar form: 1. Calculate the magnitude

r

using the formula

r = |z| = \sqrt{a^2 + b^2}

r = |z| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5.

2. Calculate the argument

\theta

using the formula

\theta = \arctan\left(\frac{b}{a}\right)

\theta = \arctan\left(\frac{4}{3}\right) \approx 0.93 \text{ radians}.

Therefore, the complex number

z = 3 + 4i

in polar form is

z = 5(\cos(0.93) + i\sin(0.93))

. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Victoria Allen on Solvelet

1. Convert the complex number

3 + 4i

to polar form.2. Find the product of the complex numbers

(1 + i)

and

(2 - i)

in polar form.

DefinitionThe polar form is the representation of a complex number in terms of modulus and argument. In other words, a complex number z can be represented as z=r(cosθ+isinθ) or z=reiθ. Eg: 1 + i = 2eiπ/4 (polar form of a complex number)

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