Rewrite the complex number in polar form

Question

Rewrite the complex number in polar form, z=r(cos(theta)+isin(theta)).
z = 2 = ?

 

A. 2(cos(0)+isin(0))

B. 2(cos(pi/4)+isin(pi/4))

C. (sqrt 2)(cos(0)+isin(0))

D. (sqrt 2)(pi/4)+isin(pi/4))

Answer 1

Hi Zachariah,

 

Remember that we can write every complex number in the form:

• z = x + iy,

where x is the real part of z, and y is the imaginary part of z.

 

If z = 2 (or z = 2 + i*0), then the real part of z is 2, and the imaginary part of z is 0 (there's no imaginary part of this z). So:

• x = 2,
• y = 0.

 

Now, the question wants us to rewrite z in polar form:

• z = r(cos θ + i sin θ).

If you distribute the r into the parenthesis, you'll end up with:

• z = r cos θ + i r sin θ.

In the above expression, the real part of z is in the first term, and the imaginary part in the second term:

• x = r cos θ,
• y = r sin θ.

 

Now we can equate our expressions for x and y:

• 2 = r cos θ,
• 0 = r sin θ.

 

We have here a system of two equations with two unknowns. Solve for r and θ using any method you like. Best of luck!