Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
-$$\frac { 4 \mathrm { i } } { 1 - 10 \mathrm { i } }$$
A) $- \frac { 40 } { 101 } + \frac { 4 } { 101 } \mathrm { i }$

B) $\frac { 40 } { 99 } - \frac { 4 } { 99 } \mathrm { i }$

C) $- \frac { 40 } { 99 } - \frac { 4 } { 99 } \mathrm { i }$

D) $\frac { 40 } { 101 } + \frac { 4 } { 101 } \mathrm { i }$

Question

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
-$$\frac { 4 \mathrm { i } } { 1 - 10 \mathrm { i } }$$
A) $- \frac { 40 } { 101 } + \frac { 4 } { 101 } \mathrm { i }$

B) $\frac { 40 } { 99 } - \frac { 4 } { 99 } \mathrm { i }$

C) $- \frac { 40 } { 99 } - \frac { 4 } { 99 } \mathrm { i }$

D) $\frac { 40 } { 101 } + \frac { 4 } { 101 } \mathrm { i }$

Quizplus · Accepted Answer

To solve $\frac { 4 \mathrm { i } } { 1 - 10 \mathrm { i } }$, first convert both the numerator and denominator into trigonometric form. The numerator $4i$ can be seen as $0 + 4i$, which has a magnitude of $4$ and an angle of $\frac{\pi}{2}$ because it lies on the positive imaginary axis. The denominator $1 - 10i$ has a magnitude of $\sqrt{1^2 + (-10)^2} = \sqrt{101}$ and an angle $\tan^{-1}(\frac{-10}{1})$, which is in the fourth quadrant. After converting to trigonometric form, divide the magnitudes and subtract the angles. Finally, convert back to rectangular form to get $- \frac { 40 } { 101 } + \frac { 4 } { 101 } \mathrm { i }$.

Find the Quotient and Write in Rectangular Form 4i1−10i\frac { 4 \mathrm { i } } { 1 - 10 \mathrm { i } }1−10i4i​

Find the Quotient and Write in Rectangular Form $\frac { 4 \mathrm { i } } { 1 - 10 \mathrm { i } }$