If {z_1} and {z_2} are any two complex number | vedclass

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(B) We use the property of complex numbers: $|z|^2 = z \bar{z}$.$|{z_1} + {z_2}|^2 + |{z_1} - {z_2}|^2 = ({z_1} + {z_2})(\overline{{z_1} + {z_2}}) + (

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$2|{z_1}|^2 + 2|{z_2}|^2$

Vedclass · Answer

(B) We use the property of complex numbers: $|z|^2 = z \bar{z}$.$|{z_1} + {z_2}|^2 + |{z_1} - {z_2}|^2 = ({z_1} + {z_2})(\overline{{z_1} + {z_2}}) + ({z_1} - {z_2})(\overline{{z_1} - {z_2}})$$= ({z_1} + {z_2})(\bar{{z_1}} + \bar{{z_2}}) + ({z_1} - {z_2})(\bar{{z_1}} - \bar{{z_2}})$$= ({z_1}\bar{{z_1}} + {z_1}\bar{{z_2}} + {z_2}\bar{{z_1}} + {z_2}\bar{{z_2}}) + ({z_1}\bar{{z_1}} - {z_1}\bar{{z_2}} - {z_2}\bar{{z_1}} + {z_2}\bar{{z_2}})$$= 2{z_1}\bar{{z_1}} + 2{z_2}\bar{{z_2}}$$= 2|{z_1}|^2 + 2|{z_2}|^2$

If ${z_1}$ and ${z_2}$ are any two complex numbers,then $|{z_1} + {z_2}|^2 + |{z_1} - {z_2}|^2$ is equal to:

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