Question Video: Converting Complex Numbers from Polar to Algebraic Form | Nagwa Question Video: Converting Complex Numbers from Polar to Algebraic Form | Nagwa

Question Video: Converting Complex Numbers from Polar to Algebraic Form Mathematics • Third Year of Secondary School

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Express 12 [cos (5π/6) + π sin (5π/6)] in algebraic form.

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Video Transcript

Express 12 multiplied by cos five π over six plus π sin five π over six in algebraic form.

This complex number is given in polar or trigonometric form. It has a modulus of 12 and an argument of five π over six. 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 and π is the imaginary component of this complex number.

We can use these conversion formulae for converting the polar coordinates with the modulus of π and an argument of π into the corresponding rectangular form. π is equal to π cos π and π is equal to π sin π.

Letβs substitute what we know about our complex number, thatβs π and π, into the conversion formulae. π is equal to 12 multiplied by cos five π over six, which is negative six root three. π is equal to 12 multiplied by sin of five π over six, which is six. Now that we have the values for π and π, we can write our complex number in algebraic form.

Since π is negative six root three and π is six, our complex number π can be written as negative six root three plus six π.

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