# Products and quotients of complex numbers

|z_{1}z_{2}| = r_{1}r_{2}, arg(z_{1}z_{2}) = y_{1} + y_{2}

|z_{1}/z_{2}| = r_{1}/r_{2}, arg(z_{1}/z_{2}) = y_{1} – y_{2}

**Question**

Given that z_{1} = 5 + 3i and z_{2} = 2-2i. Determine the following in the form of r(cos x + sin x i).

- z
_{1}z_{2} - z
_{1}/z_{2}

**Answer**

- √272(cos 0.921π + sin 0.921π i)
- √(34/8)(cos -0.579π + sin -0.579π i)

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