Free Study Material

NCERT Solutions

NCERT Books

Revision Notes

Practice Problems

This is the second of our many quizzes on Adding and subtracting complex numbers. Click on this to access more such competitive quizzes on Number System.

Adding and subtracting complex numbers Quiz 2

mathematics

 What is the summation of $3+2i$ and $5+7i$?

 A complex number has a real part and an imaginary part. For calculating summation we have to perform the addition operation.

$\begin{align} &nbsp;&nbsp;& \text{Here we have to calculate summation of }3+2i\text{ and }5+7i\text{.} \\ &nbsp;& \text{Means perform the addition operation between these two}\text{. That is} \\ &nbsp;& \left( 3+2i \right)+\left( 5+7i \right)=\left( 3+5 \right)+\left( 2i+7i \right)=8+9i. \\ \end{align}$

 Subtract the complex number $9-7i$ from $2+i$.

 To determine subtraction of two complex numbers subtract the real part and the imaginary part separately.

$\begin{align} &nbsp;&nbsp;& \text{Have to subtract the complex number }9-7i\text{ from }2+i\text{. For this perform subtraction} \\ &nbsp;& \text{operation between these two}\text{.} \\ &nbsp;& \text{That is }\left( 2+i \right)-\left( 9-7i \right)=2+i-9+7i=-7+8i. \\ \end{align}$

 Add two complex numbers $\dfrac{4}{5}+3i$ and $\dfrac{7}{10}-8i$.

 Add the real part and add the imaginary part separately.

$\begin{align} &nbsp;&nbsp;& \text{We have to perform addition operation here}\text{.} \\ &nbsp;& \text{That is add }\dfrac{4}{5}+3i\text{ with }\dfrac{7}{10}-8i\text{.} \\ &nbsp;& \left( \dfrac{4}{5}+3i \right)+\left( \dfrac{7}{10}-8i \right)=\left( \dfrac{4}{5}+\dfrac{7}{10} \right)+\left( 3i-8i \right)=\dfrac{15}{10}-5i \\ \end{align}$

 Subtract $4+5i$ from twice of the number $3-9i$.

 To get twice of a complex number multiple $2$ with that number. Then do the subtraction operation.

$\begin{align} &nbsp;&nbsp;& \text{To find twice of a complex number multiple }2\text{ with that number}\text{.} \\ &nbsp;& \text{Here }2\times \left( 3-9i \right)=6-18i. \\ &nbsp;& \text{Now }\left( 6-18i \right)-\left( 4+5i \right)=6-4-18i-5i=2-23i \\ \end{align}$

 Add a complex number $3+9i$ with thrice of the number $1-9i$. Then subtract the result from twice of $7+9i$.

 To get twice of a complex number multiple $2$ with that number. To get thrice of a complex number multiple $3$ with that number. Then do addition and subtraction operations as required.

$\begin{align} &nbsp;&nbsp;& \text{Thrice of a complex number }1-9i\text{ is }3\times \left( 1-9i \right)=3-27i\text{.} \\ &nbsp;& \text{Twice of }7+9i\text{ is }2\times \left( 7+9i \right)=14+18i\text{.} \\ &nbsp;& \text{Then addition of }3+9i\text{ and }\!\!~\!\!\text{ }3i-27\text{ }i\text{s }3+9i+3-27i=6-18i\text{.} \\ &nbsp;& \text{Then subtract }6-18i\text{ from }14+18i\text{ is }14+18i-6+18i=8+36i\text{.} \\ \end{align}$