Solve the equation .Write complex solutions in standard form.
C)

Question

Solve the equation  .Write complex solutions in standard form. ​
C) ​

Quizplus · Accepted Answer

The equation can be written as:
11eacce6_1f9c_69ab_9f49_4d8fdd43432d_TB7896_11 = x
where x is a complex number.
Taking logarithms on both sides,
ln(11) + (log_e(10)*eacce6_1f9c_69ab_9f49_4d8fdd43432d) + ln(TB7896_11)i = ln(x)
Separating the real and imaginary parts,
ln(11) + (log_e(10)*eacce6_1f9c_69ab_9f49_4d8fdd43432d) = Re(ln(x))
ln(TB7896_11) = Im(ln(x))
Using the fact that ln(e^z) = z for any complex number z, the real and imaginary parts of ln(x) can be simplified as follows:
Re(ln(x)) = ln(|x|)
Im(ln(x)) = arg(x)
Thus, the equation becomes:
ln(11) + (log_e(10)*eacce6_1f9c_69ab_9f49_4d8fdd43432d) = ln(|x|)
ln(TB7896_11) = arg(x)
To solve for x, we first find |x| and arg(x).
Using the given equation for |x|, we get:
|x| = e^(ln(11) + (log_e(10)*eacce6_1f9c_69ab_9f49_4d8fdd43432d))
Simplifying this expression, we get:
|x| = 11*10^(eacce6_1f9c_69ab_9f49_4d8fdd43432d)
Using the given equation for arg(x), we get:
arg(x) = TB7896_11
Thus, the complex solution in standard form is:
x = 11eacce6_1f9c_b7cf_9f49_0dbaf1ff4562_TB7896_11

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