Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

z=5+7i Find the angle theta (in radians) that z makes in the complex plane. Round your answer, if necessary, to the nearest thousandth. Express theta between -pi and pi. theta=

z=5+7i z=5+7 i \newlineFind the angle θ \theta (in radians) that z z makes in the complex plane. Round your answer, if necessary, to the nearest thousandth. Express θ \theta between −π -\pi and π \pi .\newlineθ= \theta=

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Find trigonometric ratios using a Pythagorean or reciprocal identityright chevron icon

Full solution

Q. z=5+7i z=5+7 i \newlineFind the angle θ \theta (in radians) that z z makes in the complex plane. Round your answer, if necessary, to the nearest thousandth. Express θ \theta between −π -\pi and π \pi .\newlineθ= \theta=
  1. Identify Parts of zz: Identify the real and imaginary parts of the complex number zz.z=5+7iz = 5 + 7i, where the real part is 55 and the imaginary part is 77.
  2. Calculate Angle Theta: Calculate the angle theta using the arctangent function.\newlineThe angle theta in the complex plane is given by the arctangent of the imaginary part divided by the real part, which is arctan⁡(75)\arctan(\frac{7}{5}).
  3. Use Arctangent Function: Use a calculator to find the value of arctan⁡(75)\arctan(\frac{7}{5}).θ=arctan⁡(75)≈0.9505\theta = \arctan(\frac{7}{5}) \approx 0.9505 radians. Since the complex number is in the first quadrant (both real and imaginary parts are positive), the angle is positive and there is no need to adjust the range.

More problems from Find trigonometric ratios using a Pythagorean or reciprocal identity

Question
If cos⁡(θ)=817 \cos(\theta)=\frac{8}{17} and 0∘<θ<90∘ 0^\circ<\theta<90^\circ , what is sec⁡(θ) \sec(\theta) ? Write your answer in simplified, rationalized form. sec⁡(θ)= \sec(\theta)= ______
Get tutor helpright-arrow

Posted 5 months ago

Question
cos⁡(x)=−0.3\cos(x) = -0.3. What is sin⁡(90∘−x)\sin(90^\circ - x)? ____
Get tutor helpright-arrow

Posted 9 months ago

Question
If csc⁡(θ)=178 \csc(\theta) = \frac{17}{8} and 0∘<θ<90∘ 0^\circ < \theta < 90^\circ , what is tan⁡(θ) \tan(\theta) ?\newlineWrite your answer in simplified, rationalized form.\newlinetan⁡(θ)= \tan(\theta) = ______\newline
Get tutor helpright-arrow

Posted 9 months ago

Question
Is the sine function even or odd?\newlineChoices:\newline[A]even\text{[A]even}\newline[B]odd\text{[B]odd}
Get tutor helpright-arrow

Posted 9 months ago

Question
Write the sentence as an equation. \newline8989 is equal to the quotient of yy and 1717 \newlineType a slash ( / / ) if you want to use a division sign. \newline_____
Get tutor helpright-arrow

Posted 7 months ago

Question
Write the sentence as an equation. \newline4545 is equal to the quotient of zz and 55 \newlineType a slash ( / / ) if you want to use a division sign. \newline_____
Get tutor helpright-arrow

Posted 9 months ago

Question
Solve for hh. \newline h2+24h=0h^2 + 24h = 0 \newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. \newline h=h = _____
Get tutor helpright-arrow

Posted 10 months ago

Question
h2−4h=0h^2 - 4h = 0
Get tutor helpright-arrow

Posted 7 months ago

Question
Combine the like terms to create an equivalent expression:\newline−k−(−8k)=□-k-(-8k)=\square
Get tutor helpright-arrow

Posted 10 months ago

Question
Which of the following degree measures is equal to 5π 5 \pi radians?\newline(The number of degrees of arc in a circle is 360360 . The number of radians of arc in a circle is 2π 2 \pi .)\newlineChoose 11 answer:\newline(A) 144∘ 144^{\circ} \newline(B) 900∘ 900^{\circ} \newline(C) 1,080∘ 1,080^{\circ} \newline(D) 1,800∘ 1,800^{\circ}
Get tutor helpright-arrow

Posted 7 months ago

View all (56)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant