ringearV

2021-02-26

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

Laaibah Pitt

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

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