NCERT Solutions for Class 11 Maths Chapter 5 Complex Number And Quadratic Equations

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Q.1: Express each of the complex number in the form a + ib. 
\((5 i)\left(-\frac{3}{5} i\right)\)

Ans : \(\begin{aligned}(5 i)\left(\frac{-3}{5} i\right) &=-5 \times \frac{3}{5} \times i \times i \\ &=-3 i^{2} \\ &=-3(-1) \\ &=3 \end{aligned}\) 

Q.2: Express each of the complex number in the form a + ib.  
\(i^{9}+i^{19}\)

Ans : \(i^{9}+i^{19}=i^{4 x-1}+i^{4 x+1}\)    
\(\begin{aligned} &=\left(i^{4}\right)^{2} \cdot j+\left(j^{4}\right)^{4} \cdot i^{3} \\ &=1 \times i+| \times(-i) \\ &=i+(-i) \\ &=0 \end{aligned}\) 

Q.3: Express each of the complex number in the form a + ib.      
\(i^{-39}\)

Ans : \(I^{-14}=f^{-1 \times 4-3}=\left(i^{4}\right)^{-9} \cdot l^{-3}\)    
\(\begin{aligned} &=(1)^{-9}-F^{-3} \\ &=\frac{1}{p^{3}}=\frac{1}{-i} \\ &=\frac{-1}{i} \times \frac{j}{i} \\ &=\frac{-i}{i^{2}}=\frac{-i}{-1}=i \end{aligned}\) 

Q.4: Express each of the complex number in the form a + ib.      
\(3(7+i 7)+i(7+i 7)\)

Ans : \(\begin{aligned} 3(7+i 7)+i(7+i 7) &=21+21 i+7 i+7 i^{2} \\ &=21+28 i+7 \times(-1) \\ &=14+28 i \end{aligned}\) 

Q.5: Express each of the complex number in the form a + ib.      
\((1-i)-(-1+i 6)\)

Ans : \(\begin{aligned}(1-i)-(-1+i 6) &=1-j+1-6 i \\ &=2-7 i \end{aligned}\) 

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All NCERT Solutions Class 11

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