====== Question 2, Exercise 1.1 ======
Solutions of Question 2 of Exercise 1.1 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 2(i)====
Write the following complex number in the form $x+iy$: $(3+2i)+(2+4i)$

** Solution. ** 

\begin{align}&(3+i2)+(2+i4)\\
=&(3+2)+(i2+i4)\\
=&5+i6\end{align}
GOOD
 ====Question 2(ii)====
Write the following complex number in the form $x+iy$: $(4+3i)-(2+5i)$

**Solution.** 

\begin{align}&(4+3i)-(2+5i)\\
=&(4-2)+(3i-5i)\\
=&2-2i\end{align}
GOOD
====Question 2(iii)====
Write the following complex number in the form $x+iy$: $(4+7i)+(4-7i)$

**Solution.** 

\begin{align}
&(4+7i)+(4-7i)\\
=&(4+4)+(7i-7i)\\
=&8+0i.
\end{align}
GOOD

====Question 2(iv)====
Write the following complex number in the form $x+iy$: $(2+5i)-(2-5i)$

**Solution.**

\begin{align}
&(2+5i)-(2-5i)\\
=&(2-2)+(5i+5i)\\
=&0+10i.
\end{align}
GOOD

====Question 2(v)====
Write the following complex number in the form $x+iy$: $(3+2i)(4-3i)$

**Solution.** 

\begin{align}&(3+2i)(4-3i)\\
=&12-9i+8i-6i^2\\
=&12+6-9i+8i\\
=&18-i\end{align}
GOOD
====Question 2(vi)====
Write the following complex number in the form $x+iy$: $(3,2)\div(3,-1)$

**Solution.**

\begin{align}&(3,2)\div(3,-1)\\
=&\dfrac{3+2i}{3-i}\\
=&\dfrac{3+2i}{3-i}\times\dfrac{3+i}{3+i}\\
=&\dfrac{(3+2i)(3+i)}{3^2-i^2}\\
=&\dfrac{9+2i^2+6i+3i}{9+1}\\
=&\dfrac{9-2+9i}{10}\\
=&\dfrac{7+9i}{10}\\
=&\dfrac{7}{10}+\dfrac{9}{10}i\end{align}
GOOD

====Question 2(vii)====
Write the following complex number in the form $x+iy$: $(1+i)(1-i)(2+i)$

**Solution.**

\begin{align}&(1+i)(1-i)(2+i)\\
=&(1+i)(2-i^2+i-2i)\\
=&(1+i)(2+1-i)\\
=&(1+i)(3-i)\\
=&3-i^2+3i-i\\
=&4+2i\end{align}

====Question 2(viii)====
Write the following complex number in the form $x+iy$: $\dfrac{1}{2+3i}$.

**Solution.**

\begin{align}
&\dfrac{1}{2+3i} \\
=&\dfrac{1}{2+3i}\times\dfrac{2-3i}{2-3i} \\
=&\dfrac{2-3i}{4-9i^2}\\
=&\dfrac{2-3i}{4+9}\\
=&\dfrac{2}{13}-\dfrac{3}{13}i.\\
\end{align}
GOOD
====Go to ====

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<text align="right"><btn type="success">[[math-11-nbf:sol:unit01:ex1-1-p3|Question 3 >]]</btn></text> ======