simplify |x+yi|^2

Solution

simplify

∣ x + y i ∣^{2}

x^{2} + y^{2}

Solution steps

∣ x + y i ∣^{2}

Apply complex arithmetic rule:

∣ a + bi ∣ = a^{2} + b^{2}

∣ x + y i ∣ = x^{2} + y^{2}

= (x^{2} + y^{2})^{2}

Apply radical rule:

a = a^{\frac{1}{2}}

= ((x^{2} + y^{2})^{\frac{1}{2}})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= (x^{2} + y^{2})^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

= x^{2} + y^{2}

\frac{13800}{3}

\frac{4}{9}

6 \times \frac{5}{4}

\frac{9}{16} + \frac{4}{128}

\frac{3 - 3}{6 - 3}