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

Square Complex Number Calculation: To square the complex number (3+2i), we will use the formula (a+bi)^2 = a^2 + 2abi - b^2, where a=3 and b=2. Calculation: (3+2i)^2 = 3^2 + 2*3*2i - (2i)^2Square Real Part: First, we square the real part, which is 3. Calculation: 3^2 = 9Calculate Imaginary Coefficient: Next, we calculate the coefficient of the imaginary part, which is 2 times a times b. Calculation: 2*3*2 = 12, so the imaginary part is 12i.Square Imaginary Part: Finally, we square the imaginary part, which is 2i, and subtract it from the real part since i^2 = -1. Calculation: (2i)^2 = 4i^2 = 4*(-1) = -4Combine All Parts: Now, we combine all parts to get the final result. Calculation: 9 + 12i - 4 = 5 + 12i

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

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

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Algebra 2

Csc, sec, and cot of special angles

Full solution

Q. Write

(3+2 i)^{2}

in simplest

a+b i

form.

\newline

Answer:

Square Complex Number Calculation: To square the complex number $(3+2i)$ , we will use the formula $(a+bi)^2 = a^2 + 2abi - b^2$ , where $a=3$ and $b=2$ . $\newline$ Calculation: $(3+2i)^2 = 3^2 + 2\cdot3\cdot2i - (2i)^2$
Square Real Part: First, we square the real part, which is $3$ . $\newline$ Calculation: $3^2 = 9$
Calculate Imaginary Coefficient: Next, we calculate the coefficient of the imaginary part, which is $2$ times $a$ times $b$ . $\newline$ Calculation: $2\times3\times2 = 12$ , so the imaginary part is $12i$ .
Square Imaginary Part: Finally, we square the imaginary part, which is $2i$ , and subtract it from the real part since $i^2 = -1$ . $\newline$ Calculation: $(2i)^2 = 4i^2 = 4*(-1) = -4$
Combine All Parts: Now, we combine all parts to get the final result. $\newline$ Calculation: $9 + 12i - 4 = 5 + 12i$