# Question Video: Writing a Complex Number in Polar Form given Its Modulus and Principal Argument Mathematics • 12th Grade

Given that |π| = 8 and the argument of π is π = 360Β°, find π, giving your answer in trigonometric form.

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### Video Transcript

Given that the modulus of π is equal to eight and the argument of π is π equals 360 degrees, find π, giving your answer in trigonometric form.

When we write a complex number in trigonometric or polar form, we write it as π is equal to π multiplied by cos π plus π sin π, where π is the modulus of the complex number π and π is its argument. In polar form, π can be in degrees or radians, though radians is often preferred, whereas in exponential form, it does need to be in radians.

Weβre going to substitute what we know about the complex number π into this formula. But before we do, letβs convert the argument into radians. To change from degrees into radians, we can multiply by π over 180. 360 multiplied by π over 180 is two π. So 360 degrees is two π radians, although this is a standard result we shouldβve known by heart.

So we can now substitute what we know into the formula for the trigonometric form or the polar form of a complex number. And doing so, we can see that π is equal to eight multiplied by cos of two π plus π sin of two π.