Question

What is $5i$ equal to?

Answer 1

Complex numbers:

Complex numbers are expressed in the form of $x+iy$ where $x\mathrm{and}y$ are real parts and imaginary parts of complex number respectively, and $\mathrm{i}$ is an imaginary number.

$5\mathrm{i}$ is a complex number and we can write it in the general form as $0+5\mathrm{i}$ and also known as purely imaginary.

Therefore,

$5i=5\sqrt{-1}$ $\left[\because i=\sqrt{-1}\right]$

$\Rightarrow$ $5i=\sqrt{25}\sqrt{-1}$

$\Rightarrow$ $5i=\sqrt{-25}$ $\left[\because \sqrt{a}\sqrt{b}=\sqrt{ab}\right]$

Hence, the value of $\mathbf{5}\mathbf{i}$ is $\sqrt{\mathbf{-}\mathbf{25}}$ .