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If $a=2$ and $b=2i$ , then find the value of the $ab^{3}$ in fully simplified form.

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Evaluate expression when two complex numbers are given

Full solution

Q. If

a=2

and

b=2i

, then find the value of the

ab^{3}

in fully simplified form.

Given values substitution: We are given: $\newline$ $a = 2$ $\newline$ $b = 2i$ $\newline$ We need to find the value of the expression $ab^{3}$ . $\newline$ First, let's substitute the given values of $a$ and $b$ into the expression. $\newline$ $ab^{3} = 2 \times (2i)^{3}$
Expression simplification: Now, let's simplify the expression $(2i)^{3}$ . $(2i)^{3} = (2^3) \cdot (i^3)$ = $8 \cdot i^3$ Since $i^2 = -1$ , we can simplify $i^3$ as $i^2 \cdot i = -1 \cdot i = -i$ .So, $(2i)^{3} = 8 \cdot -i$ = $-8i$
Final simplification: Next, we multiply the result from the previous step by $2$ . $\newline$ $2 \times -8i = -16i$ $\newline$ This is the fully simplified form of the expression $ab^{3}$ .

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