What is expand log_{10}((1+i*sqrt(3))^{2022}) ?

The solution to expand log_{10}((1+i*sqrt(3))^{2022}) is 2022log_{10}(1+isqrt(3))

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expand log_{10}((1+i*sqrt(3))^{2022})

expand

lo g_{10} ((1 + i \cdot 3)^{2022})

2022 lo g_{10} (1 + i 3)

Solution steps

lo g_{10} ((1 + i 3)^{2022})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{10} ((1 + i 3)^{2022}) = 2022 lo g_{10} (1 + i 3)

= 2022 lo g_{10} (1 + i 3)

2 ln (5) + (- \frac{1}{5}) + 3 ln (6) - (- 2 ln (1) - 1 + 3 ln (2))

- lo g_{10} (6.656 \cdot 1 0^{- 5})

(\frac{1}{2}) (ln (11 + 22 (6)) - ln (11 - 22 (6)))

\frac{1}{2} lo g_{12} (2)

ln (6 sec (x))

What is expand log_{10}((1+i*sqrt(3))^{2022}) ?
The solution to expand log_{10}((1+i*sqrt(3))^{2022}) is 2022log_{10}(1+isqrt(3))