[SPLIT] z = 2 + 2i: how to express z^2 in polar form

[niallm]

How do you find out what theta for cos and sin are in the formula? So let's say we have z = 2 + 2i, where z² = 4 + 8i + 4i² = 8i in the form a + bi. How do you express z² in polar form? I put down z² = 8(cos(pi/2) + i sin(pi/2)). Is this correct?

 

[stapel]

How do you find out what theta for cos and sin are in the formula?

To learn, in general, how to convert between Cartesian, polar, and exponential forms, try online lessons such as this.

So let's say we have z = 2 + 2i, where z² = 4 + 8i + 4i² = 8i in the form a + bi. How do you express z² in polar form? I put down z² = 8(cos(pi/2) + i sin(pi/2)). Is this correct?

If you're not sure, evaluate! What is the cosine of pi/2? What is the sine of pi/2? When you plug these values in, what do you get in the simplified form?