Question

Express (-5i ) (
1/8i) in the form of a+ib.​

Answer 1

☆ Given Question :-

• Express (-5i ) (1/8i) in the form of a+ib.

$\huge \orange{AηsωeR} ✍$

$\begin{gathered}\begin{gathered}\bf{\underline{\underline{Given :-}}}\end{gathered}\end{gathered}$

$\bf \: - 5i(\dfrac{1}{8i} )$

$\begin{gathered}\begin{gathered}\bf{\underline{\underline{To Find :-}}}\end{gathered}\end{gathered}$

$\bf \:Express \: in \: standard \: form$

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$\begin{gathered}\begin{gathered}\bf{\underline{\underline{Theory :-}}}\end{gathered}\end{gathered}$

A complex number is a number that can be expressed in the form a + bi,

where a and b are real numbers, and i represents the imaginary unit,

satisfying the equation i² = −1.

Because no real number satisfies this equation, i is called an imaginary number. 

The complex numbers z = a + bi, consisting of two parts: The real part : represented as Re(z) = a.

The imaginary part : representedas Im(z) = b.

When Re(z) = 0, we say that z is purely imaginary;

when Im(z) = 0, we say that z is purely real.

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$\begin{gathered}\begin{gathered}\bf{\underline{\underline{Solution :-}}}\end{gathered}\end{gathered}$

$\bf \: - 5i \times (\dfrac{1}{8i} )$

$\bf \:  ⟼ - \dfrac{5}{8} {i}^{2}$

$\bf \:  ⟼ - \dfrac{5}{8} \times ( - 1)$

$\bf \:  ⟼ \dfrac{5}{8}$

$\bf \:  ⟼ \dfrac{5}{8} + 0i$

$\large{\boxed{\boxed{\bf{Hence,- 5i \times (\dfrac{1}{8i}) = \dfrac{5}{8} + 0i}}}}$