how do I write z1 in polar form: z1= 1+ √(3) * i 

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You need to convert the given algebraic form of the complex number `z_1` in polar form, such that:

`z_1 = |z_1|(cos alpha + i sin alpha)`

You need to determine the absolute value of `z_1` such that:

`|z_1| = sqrt(1^2 + (sqrt3)^2)`

`|z_1| = sqrt(1+3) => |z_1| = sqrt(4) =>...

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You need to convert the given algebraic form of the complex number `z_1` in polar form, such that:

`z_1 = |z_1|(cos alpha + i sin alpha)`

You need to determine the absolute value of `z_1` such that:

`|z_1| = sqrt(1^2 + (sqrt3)^2)`

`|z_1| = sqrt(1+3) => |z_1| = sqrt(4) => |z_1| = 2`

`tan alpha = (sqrt3)/1 => tan alpha = sqrt3 => alpha = pi/3`

`z_1 = 2(cos (pi/3) + i sin (pi/3))`

Hence, evaluating the polar form of the complex number `z_1 = 1 + sqrt3*i` , yields `z_1 = 2(cos (pi/3) + i sin (pi/3)).`

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