Gujarat BoardEnglish MediumSTD 11 ScienceMATHSCOMPLEX NUMBERS AND QUADRATIC EQUATIONS1 Mark
MCQ
Choose the correct answer. If $a+i b=c+i d$, then:
A
$a^2+c^2=0$
B
$b^2+c^2=0$
C
$b^2+d^2=0$
✓
$a^2+b^2=c^2+d^2$
✓
Answer
Correct option: D.
$a^2+b^2=c^2+d^2$
$a^2+b^2=c^2+d^2$
Solution:
Given that $\text{a}+\text{ib}=\text{c}+\text{id}$
$\Rightarrow|\text{a}+\text{ib}|=|\text{c}+\text{id}|$
$\Rightarrow\sqrt{\text{a}^2+\text{b}^2}=\sqrt{\text{c}^2+\text{d}^2}$
Squaring both sides, we get $a^2+b^2=c^2+d^2$
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