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le of
a in these diagrams.
b
C

le of $a$ in these diagrams. $\newline$ b $\newline$ C

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Evaluate expression when two complex numbers are given

Full solution

Q. le of

a

in these diagrams.

\newline

b

\newline

C

Plug values into expression: We know $a = 2$ and $b = 2i$ , so plug these into the expression $ab^{3}$ . $\newline$ Calculation: $2 \times (2i)^{3}$
Calculate power of $(2i)$ : Calculate $(2i)^{3}$ by raising both the coefficient and the imaginary unit to the power of $3$ . $\newline$ Calculation: $(2^{3}) \cdot (i^{3})$
Simplify powers: Simplify the powers. $\newline$ Calculation: $8 \times i^3$
Use $i^2 = -1$ : Remember that $i^2 = -1$ , so $i^3 = i^2 \cdot i = -1 \cdot i$ . $\newline$ Calculation: $8 \cdot (-1 \cdot i)$
Multiply by -i: Multiply $8$ by $-i$ . $\newline$ Calculation: $8 \times -i = -8i$
Multiply by $2$ : Now multiply the result by $2$ from the first step. $\newline$ Calculation: $2 \times -8i$
Simplify multiplication: Simplify the multiplication. $\newline$ Calculation: $-16i$

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