# Question 10, Exercise 1.4

Solutions of Question 10 of Exercise 1.4 of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

## Question 10(i)

Find the impedance $Z$ for the following values: $E=(-50+100 i)$ volts, $I=(-6-2 i)$ amps.

** Solution. **

Here we have $E=(-50+100 i)$ volts

$I=(-6-2 i)$ amps.

Using the formula $$ E = I \times Z $$ $$(-50+100 i)= (-6-2 i) \times Z $$ \begin{align} \implies Z & = \dfrac{-50+100 i}{-6-2 i} \\ & = \dfrac{(-50+100 i)(-6+2i)}{(-6-2 i)(-6+2i)}\\ & = \dfrac{300-200-100i-600i}{36+4}\\ & = \dfrac{100-700i}{40}\\ & = 25-175i.\\ \end{align} Hence, impedance $Z=25-175i$.

## Question 10(ii)

Find the impedance $Z$ for the following values: $E=(100+10 i)$ volts, $I=(-8+3 i) \mathrm{amps}$

** Solution. **

*Do yourself as above*

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