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Question

Mathematics Question on Complex Numbers and Quadratic Equations

If a+ib=c+ida + ib = c + id, then

A

a2+c2=0a^{2}+c^{2}=0

B

b2+c2=0b^{2}+c^{2}=0

C

b2+d2=0b^{2}+d^{2}=0

D

a2+b2=c2+d2a^{2}+b^{2}=c^{2}+d^{2}

Answer

a2+b2=c2+d2a^{2}+b^{2}=c^{2}+d^{2}

Explanation

Solution

a+ib=c+ida + ib = c + id ∴ ∣a+ib∣=∣c+id∣\therefore\, \left|a+ib\right|=\left|c+id\right| ⇒ a2+b2=c2+d2\Rightarrow\, a^{2}+b^{2}=c^{2}+d^{2}