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  • Express each of the complex number in the form a+ib. (9) (1/3+3i)^3

Express each of the complex number in the form  a+ib.

Q : 9    \left ( \frac{1}{3}+3i \right )^3

Answers (1)

best_answer

Given problem is 
\left ( \frac{1}{3}+3i \right )^3
Now, we will reduce it into

\left ( \frac{1}{3}+3i \right )^3=\left ( \frac{1}{3} \right )^3+(3i)^3+3.\left ( \frac{1}{3} \right )^2.3i+3.\frac{1}{3}.(3i)^2                (using \ (a+b)^3=a^3+b^3+3a^2b+3ab^2)
                        = \frac{1}{27}+27i^3+i + 9i^2                                                        
                        = \frac{1}{27}+27(-i)+i + 9(-1)                                                               (\because i^3=-i \ and \ i^2 = -1)
                        =\frac{1}{27}-27i+i-9
                        =\frac{1-243}{27}-26i
                        =-\frac{242}{27}-26i
                                                                         
Therefore, the answer is 

 -\frac{242}{27}-26i

Posted by

Gautam harsolia

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