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Express
z_(1)=0+10 i in polar form.
Express your answer in exact terms, using degrees, where your angle is between
0^(@) and
360^(@), inclusive.

z_(1)=

Express $z_{1}=0+10 i$ in polar form. $\newline$ Express your answer in exact terms, using degrees, where your angle is between $0^{\circ}$ and $360^{\circ}$ , inclusive. $\newline$ $z_{1}=$

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Find the inverse of a linear function

Full solution

Q. Express

z_{1}=0+10 i

in polar form.

\newline

Express your answer in exact terms, using degrees, where your angle is between

0^{\circ}

and

360^{\circ}

, inclusive.

\newline

z_{1}=

Calculate Magnitude: To express a complex number in polar form, we need to find its magnitude $r$ and angle $\theta$ in degrees. The magnitude is the distance from the origin to the point in the complex plane, which can be calculated using the Pythagorean theorem. $\newline$ Calculation: $r = \sqrt{\text{Re}(z_1)^2 + \text{Im}(z_1)^2} = \sqrt{0^2 + 10^2} = \sqrt{100} = 10$
Find Angle: Next, we need to find the angle $\theta$ . For a complex number $a + bi$ , the angle $\theta$ is given by $\theta = \text{arctan}(\frac{b}{a})$ . However, since the real part ( $a$ ) is $0$ , we need to determine the angle based on the sign of the imaginary part ( $b$ ). Since $b$ is positive and $a$ is $0$ , the angle $\theta$ is $a + bi$ $1$ degrees, which is the angle for the positive imaginary axis. $\newline$ Calculation: $a + bi$ $2$ (since we are directly above the origin on the imaginary axis)
Express in Polar Form: Now we can express the complex number $z_1$ in polar form. The polar form is given by $z = r(\cos(\theta) + i\sin(\theta))$ , where $r$ is the magnitude and $\theta$ is the angle. $\newline$ Calculation: $z_1 = 10(\cos(90°) + i\sin(90°))$

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