JEE Advance - Mathematics (1988 - No. 10)
$$\,{\left| {a{z_1} - b{z_2}} \right|^2} + {\left| {b{z_1} + a{z_2}} \right|^2} = .........$$
$$\left( {{a^2} - {b^2}} \right)left( {{{\left| {{z_1}} \right|}^2} - {{\left| {{z_2}} \right|}^2}} \right)$$
$$\left( {{a^2} + {b^2}} \right)left( {{{\left| {{z_1}} \right|}^2} - {{\left| {{z_2}} \right|}^2}} \right)$$
$$\left( {{a^2} - {b^2}} \right)left( {{{\left| {{z_1}} \right|}^2} + {{\left| {{z_2}} \right|}^2}} \right)$$
$$\left( {{a^2} + {b^2}} \right){\left| {{z_1} + {z_2}} \right|^2}$$
$$\left( {{a^2} + {b^2}} \right)left( {{{\left| {{z_1}} \right|}^2} + {{\left| {{z_2}} \right|}^2}} \right)$$
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