Question

Express the following in the form of $a+bi$
(i) $(-i)\left(2i\right){\left(-\frac{1}{8}i\right)}^3$

Answer 1

$\left(2i\right){\left(-\frac{1}{8}i\right)}^3$

$=-2i^2{\left(-\frac{1}{8}\right)}^3.i^3$

$=2\left(-\frac{1}{512}\right)(-i)\left[i^2=-1,i^3=i^2.i=-1.i=-i\right]$

$=2\times \frac{1}{512}\times i$

$=\frac{i}{256}=\left(0+\frac{1}{256}i\right)$

$Herea=0,b=\frac{1}{256}$