Question

1. $(6-7i)^2$
2. $(2-5i)(2+5i)$

Explanation:

Step1: Expand using square formula

$(a-b)^2 = a^2 - 2ab + b^2$, so:
$(6-7i)^2 = 6^2 - 2\times6\times7i + (7i)^2$

Step2: Calculate each term

$6^2=36$, $2\times6\times7i=84i$, $(7i)^2=49i^2=-49$

Step3: Combine real and imaginary parts

$36 - 84i - 49 = (36-49) - 84i$

Step4: Simplify real part

$-13 - 84i$

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Step1: Use difference of squares formula

$(a-b)(a+b)=a^2-b^2$, so:
$(2-5i)(2+5i)=2^2 - (5i)^2$

Step2: Calculate each term

$2^2=4$, $(5i)^2=25i^2=-25$

Step3: Simplify the expression

$4 - (-25) = 4 + 25$

Step4: Compute final sum

$29$

Answer:

1. $-13 - 84i$
2. $29$