Question

Find the non zero integral.Solution of | 1 - i |^x = 2^x​

Answer 1

$<b> <i> <u> Heya! </i> </u> </b>$

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★$<b> <u> Complex Number System </u> </b>$★

$= > find \: the \: non \: zero \: integral \: solutions \: of = \\ \\ = > \: |1 - i| {}^{x} = 2 {}^{x} \\ \\ = > ( \sqrt{2} ) {}^{x} = 2 {}^{x} \\ \\ = > 2 {}^{ \frac{x}{2} } = 1 \\ \\ = > 2 {}^{ \frac{x}{2} } = 2 {}^{0} \\ \\ = > \frac{x}{2} = 0$

•°• $<b> <u> x = 0 </b> </u>$

→ The Equation has no integral solution !!
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Answer 2

Step-by-step explanation:

| 1 -i|^x = 2^x

we know,

|a + ib| = √(a² + b²) use this concept here,

so, |1 - i| = √{1² + (-1)²}

= √(1 + 1) = √2

now,

| 1 - i|^x = 2^x

(√2)^x = 2^x

(2½)^x = 2^x

2^(x/2) = 2^x

x/2 = x

x/2 - x = 0

x/2 = 0

x = 0 but we need non-zero solutions

here, we see , there is no non-zero solution.

so, number of solutions is zero.