Question

Simplify the expression below then match them to the appropriate answer.

Answer 1

The given expression as;

a)

$\begin{gathered} \sqrt[]{-1024}=\sqrt[]{-1}\sqrt[]{1024} \\ \text{ SInce, }1024=32\times32 \\ 1024=32^2 \\ \sqrt[]{-1024}=\sqrt[]{-1}\sqrt[]{32^2} \\ \sqrt[]{-1024}=32i \end{gathered}$

b)

$\begin{gathered} (5i)(2i)=5\times2i\times i \\ (5i)(2i)=10i^2 \\ As,i^2=-1 \\ \mleft(5i\mright)\mleft(2i\mright)=-10 \end{gathered}$

c)

$\begin{gathered} \sqrt[]{-100}=\sqrt[]{-1}\sqrt[]{100} \\ As,\sqrt[]{-1}=i\text{ and }\sqrt[]{100}=\sqrt[]{10^2}=10 \\ \sqrt[]{-100}=\sqrt[]{-1}\sqrt[]{100} \\ \sqrt[]{-100}=10i \end{gathered}$

d)

$\begin{gathered} (4i)^2(2i)=(4^2i^2)(2i) \\ \text{ Since, i}^2=-1 \\ (4i)^2(2i)=4\times4(-1)2i \\ (4i)^2(2i)=-16(2i) \\ (4i)^2(2i)=-32i \end{gathered}$

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