# Find the product of the complex numbers.Leave answers in polar form. z_1 = 1 + i z_2 = -1 + i

Question
Complex numbers
Find the product of the complex numbers.Leave answers in polar form.
$$\displaystyle{z}_{{1}}={1}+{i}$$
$$\displaystyle{z}_{{2}}=-{1}+{i}$$

2021-02-27
To find the product of the given complex numbers.
Solution:
The product for the complex numbers can be calculated as
$$\displaystyle{z}_{{1}}\cdot{z}_{{2}}={\left({1}+{i}\right)}\cdot{\left(-{1}+{i}\right)}={i}^{{2}}-{1}^{{2}}=-{1}-{1}=-{2}$$
The product of the complex numbers is obtained as, (−2) and can be written in polar form as,
$$\displaystyle{z}_{{1}}\cdot{z}_{{2}}=-{2}{z}_{{1}}\cdot{z}_{{2}}=-{2}{\left({{\cos{{0}}}^{\circ}+}{i}{\sin{{0}}}^{\circ}\right)}$$
Hence, the product for the given complex numbers is obtained as $$\displaystyle-{2}{\left({{\cos{{0}}}^{\circ}+}{i}{\sin{{0}}}^{\circ}\right)}$$

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