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Write
(9-2i)^(2) in simplest
a+bi form.
Answer:

Write $(9-2 i)^{2}$ in simplest $a+b i$ form. $\newline$ Answer:

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Csc, sec, and cot of special angles

Full solution

Q. Write

(9-2 i)^{2}

in simplest

a+b i

form.

\newline

Answer:

Calculate $(9-2i)^2$ : To square the complex number $(9-2i)$ , we will use the formula $(a-bi)^2 = a^2 - 2abi + (bi)^2$ . Let's calculate $(9-2i)^2$ : $(9-2i)^2 = 9^2 - 2\cdot9\cdot2i + (2i)^2$
Compute each term: Now we will compute each term separately: $\newline$ $9^2 = 81$ $\newline$ $-2 \times 9 \times 2i = -36i$ $\newline$ $(2i)^2 = -4$ (since $i^2 = -1$ )
Combine terms: Combine the terms to get the result in $a+bi$ form: $\newline$ $81 - 36i - 4$
Simplify expression: Simplify the expression by combining like terms: $81 - 4 = 77$ So, the expression becomes $77 - 36i$
Final answer: The final answer in $a+bi$ form is: $77 - 36i$

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