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Simplify $(5+2i)(1+3i)$ . $\newline$ A. $5+6i$ $\newline$ B. $-1$ $\newline$ C. $-1+17 i$ $\newline$ D. $11+17 i$

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Simplify radical expressions with variables

Full solution

Q. Simplify

(5+2i)(1+3i)

.

\newline

A.

5+6i

\newline

B.

-1

\newline

C.

-1+17 i

\newline

D.

11+17 i

Identify and Apply Distributive Property: Identify the given expression and apply the distributive property (also known as the FOIL method for binomials) to multiply the two complex numbers. $\newline$ $(5+2i)(1+3i) = 5\cdot(1) + 5\cdot(3i) + 2i\cdot(1) + 2i\cdot(3i)$
Perform Multiplication for Each Term: Perform the multiplication for each term. $\newline$ $5\times(1) = 5$ $\newline$ $5\times(3i) = 15i$ $\newline$ $2i\times(1) = 2i$ $\newline$ $2i\times(3i) = 6i^2$ $\newline$ Remember that $i^2 = -1$ .
Substitute and Combine Like Terms: Substitute $i^2$ with $-1$ and combine like terms. $\newline$ $5 + 15i + 2i + 6(-1) = 5 + 17i - 6$
Simplify Real and Imaginary Parts: Simplify the real and imaginary parts. $\newline$ $(5 - 6) + 17i = -1 + 17i$

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