Complex Numbers

What is the conjugate of the complex number $$z = 4 - 5i$$ ?

Graph $$z = 3 + 4i$$ , what is the modulus $$|z|$$ ?

Write the polar form of the complex number $$z = 1 + i$$ ?

What is the distance between the complex numbers $$z_1 = 1 + 2i$$ and $$z_2 = 4 + 6i$$ in the complex plane?

(a)  

Write the complex number in polar form. Please use radians.

$$2\sqrt[]{3}\ +2i$$

Convert to rectangular form.

$$8\left(\cos\left(\frac{11\pi}{6}\right)+i\sin\left(\frac{11\pi}{6}\right)\right)$$

Find the product. Express your answer in rectangular form.

$$4\left(\cos\left(210^o\right)+i\sin\left(210^o\right)\right)\cdot\sqrt[]{3}\left(\cos\left(120^o\right)+i\sin\left(120^o\right)\right)$$

(hint: put i in the trailer)

DIVIDE. Express your answer in rectangular form.

$$7\sqrt[]{6}\left(\cos\left(\frac{11\pi}{6}\right)+i\sin\left(\frac{11\pi}{6}\right)\right)\div$$

$$14\left(\cos\left(\frac{3\pi}{2}\right)+i\sin\left(\frac{3\pi}{2}\right)\right)$$

Exact answers put i in the trailer.

Find the power. Express your answer in rectangular form.

$$5\left(\cos\left(\frac{\pi}{2}\right)+i\sin\left(\frac{\pi}{2}\right)\right)^5$$

Find the power. Express your answer in rectangular form.

$$\left(\sqrt[]{5}\ -\ \sqrt[]{15}i\right)^6$$