Write (2+4i)^(3) in simplest a+bi form. Answer:

Expand Expression: Expand the expression (2+4i)^(3) using the binomial theorem or by multiplying (2+4i) by itself three times. Calculation: (2+4i) * (2+4i) * (2+4i)Multiply First Two Terms: Multiply the first two (2+4i) terms together. Calculation: (2+4i) * (2+4i) = 4 + 16i + 16i^2 Since i^2 = -1, we can simplify this to: 4 + 16i - 16 = -12 + 16iMultiply Result: Multiply the result from Step 2 by the remaining (2+4i) term. Calculation: (-12 + 16i) * (2+4i) = -24 + 32i - 48i + 64i^2 Again, since i^2 = -1, we can simplify this to: -24 + 32i - 48i - 64 = -88 - 16iCombine Like Terms: Combine like terms to get the expression in a+bi form. Calculation: -88 - 16i

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Write
(2+4i)^(3) in simplest
a+bi form.
Answer:

Write $(2+4 i)^{3}$ in simplest $a+b i$ form. $\newline$ Answer:

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Precalculus

Find the roots of factored polynomials

Full solution

Q. Write

(2+4 i)^{3}

in simplest

a+b i

form.

\newline

Answer:

Expand Expression: Expand the expression $(2+4i)^{3}$ using the binomial theorem or by multiplying $(2+4i)$ by itself three times. $\newline$ Calculation: $(2+4i) \times (2+4i) \times (2+4i)$
Multiply First Two Terms: Multiply the first two $(2+4i)$ terms together. $\newline$ Calculation: $(2+4i) \times (2+4i) = 4 + 16i + 16i^2$ $\newline$ Since $i^2 = -1$ , we can simplify this to: $4 + 16i - 16 = -12 + 16i$
Multiply Result: Multiply the result from Step $2$ by the remaining $(2+4i)$ term. $\newline$ Calculation: (-12 + 16i) \times (2+4i) = -24 + 32i - 48i + 64i^2$\newlineAgain, since \$i^2 = -1$, we can simplify this to: $-24 + 32i - 48i - 64 = -88 - 16i$
Combine Like Terms: Combine like terms to get the expression in $a+bi$ form.$\newline$Calculation: $-88 - 16i$