Question Video: Forming a Complex Number in Algebraic Form given Its Principal Argument and Modulus | Nagwa Question Video: Forming a Complex Number in Algebraic Form given Its Principal Argument and Modulus | Nagwa

# Question Video: Forming a Complex Number in Algebraic Form given Its Principal Argument and Modulus Mathematics • Third Year of Secondary School

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Given that |π| = 12 and the argument of π is π = 120Β°, find π, giving your answer in algebraic form.

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### Video Transcript

Given that the modulus of π is 12 and the argument of π is π which is 120 degrees, find π, giving your answer in algebraic form.

When we represent a complex number in algebraic or rectangular form, we write it as π plus ππ. We can use the following conversion formulae for converting the polar coordinates with the modulus of π and an argument π into its corresponding rectangular form. π is equal to π cos π. And π is equal to π sin π. We know that the modulus of our complex number is 12. And the argument π is 120 degrees.

Letβs substitute these values into the conversion formulae for π and π. π is 12 multiplied by cos of 120 degrees. And as long as we make sure that our calculator is in degrees mode, that gives us a value of negative six. π is 12 multiplied by sin of 120 degrees, which is six root three. This means that the rectangular or algebraic form of the complex number is negative six plus six root three π.

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