For any two complex numbers $z_{1} a n d z_{2}$ and two real numbers, a, b, find the value of $| a z_{1} - b z_{2} |^{2} + | b z_{1} + b z_{2} |^{2} .$

Open in App

Solution

$| a z_{1} - b z_{2} |^{2} + | b z_{2} + a z_{1} |^{2} . = | a z_{1} |^{2} + | b z_{2} |^{2} - 2 R e (a z_{1} . b_{2}) | b z_{1} |^{2} + | a z_{2} |^{2} + 2 R e (a z_{1} . b_{2})^{2} = (a^{2} + b^{2}) | z_{1} |^{2} + (a^{2} + b^{2}) | z_{2} |^{2} = (a^{2} + b^{2}) (| z_{1} |^{2} + | z_{2} |^{2})$

Suggest Corrections

Similar questions

z_{1}, z_{2}

| a z_{1} - b z_{2} |^{2} + | b z_{1} + a z_{2} |^{2} = . . . . .

For any two complex number $z_{1}$ and $z_{2}$ and any real numbers a and b;
$| (a z_{1} - b z_{2}) |^{2}$ + $| (b z_{1} - a z_{2}) |^{2}$ =

z_{1}, z_{2}

| a z_{1} - b z_{2} |^{2} + | b z_{1} + a z_{2} |^{2} = k (a^{2} + b^{2}) (| z_{1} |^{2} + | z_{2} |^{2})

2 k

z_{1}, z_{2}

a, b

| a z_{1} - b z_{2} |^{2} + | b z_{1} + a z_{2} |^{2} = (a^{2} + b^{2}) (| z_{1} |^{2} + | z_{2} |^{2})

Join BYJU'S Learning Program