Question

If a= 5i and b= -1+2i, then find the value of a^2b in fully simplified form

Answer 1

`\boxed{=11-2i}`

Explanation:

`a=5\mathrm{i}\\b=-1+2\mathrm{i}`

I suppose the correct expression to calculate is:

`a^2b`

so:

`\begin{aligned} a^2&=(-1+2i)^2\\&=(1-4i+4i^2)\end{aligned}`

According to the properties of imaginary numbers:
`i^2=-1`

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

Finally, we'll substitute this value in
`a^2b`

`\begin{aligned}\therefore a^2b&=(-3-4i)(-1+2i)\\&=3-6i+4i-8(-1)\\&=11-2i\\\end{aligned}`

`\text{-B$\mathfrak{randon}$VN}`