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§| = 5 and the argument of π§ is π = 270Β°, find π§, giving your answer in algebraic form.

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### Video Transcript

Given that the modulus of π§ is five and the argument of π§ is π, which is equal to 270 degrees, find π§, giving your answer in algebraic form.

When we write a complex number in algebraic or rectangular form, we write it as π plus ππ, where π is the real component of the complex number and π is the imaginary component.

We can use these conversion formulae to convert the polar coordinates with a modulus of π and an argument π into the corresponding rectangular form. π is equal to π cos π and π is equal to π sin π. The modulus of our complex number is five. And π, the argument, is 270 degrees.

Often, the argument will be given in radians. But since weβre converting a complex number into rectangular form, this doesnβt really matter, as long as we remember to make sure our calculator is working in degrees.

Letβs substitute these values into the conversion formulae for π and π. π is equal to five multiplied by cos of 270 degrees, which is zero. And π is equal to five multiplied by sin of 270 degrees, which is negative five.

In rectangular form, π plus ππ then, we can write our complex number as zero plus negative five π, which is simply negative five π.

We have expressed our complex number in algebraic or rectangular form. π§ is equal to negative five π.

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