If zr=cos(2 r π)/(4)+i sin(2 r π)/(4) where r=0,1,2,3 then (z0+z1)/(z2+z3) equals (a) 1 (b) -1 (

step 1 In this question it is given that zr is equal to cos 2r pi by 4 plus i sine 2r pi by 4 and the v

If zr=cos(2 r π)/(4)+i sin(2 r π)/(4) where r=0,1,2,3 then...

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Key Concepts

Complex Arithmetic Operations

Operations such as addition and division of complex numbers require combining or manipulating their real and imaginary parts. While addition is often performed in rectangular form, division can be facilitated by using the polar form (or exponential form), which makes handling angles and moduli more straightforward.

Roots of Unity

Roots of unity are the solutions to the equation z^n = 1. They are evenly distributed on the unit circle in the complex plane, with each root having a modulus of 1 and angles that are integer multiples of 2?/n. This concept is key when analyzing symmetries and simplifying computations involving complex numbers.

Complex Numbers in Polar Form

Complex numbers can be represented in polar form as r(cos ? + i sin ?), where r is the magnitude and ? is the angle. This form is particularly useful for multiplication, division, and finding powers or roots of complex numbers, as these operations correspond to operations on the magnitudes and angles.

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