Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the absolute value. $|-7i|$

View step-by-step help

View step-by-step help

Absolute values of complex numbers

Full solution

Q. Find the absolute value.

|-7i|

Complex Number Absolute Value Formula: The absolute value of a complex number in the form $a + bi$ is given by the formula $|a + bi| = \sqrt{a^2 + b^2}$ , where $a$ is the real part and $b$ is the imaginary part.
Substitute Real and Imaginary Parts: In the expression |\(-7i| ext{, the real part } a \text{ is } $0$ \text{ and the imaginary part } b \text{ is } $-7$ . \text{ Therefore, we substitute } a = $0$ \text{ and } b = $-7$ \text{ into the formula.} $\newline$ $|-7i| = \sqrt{0^2 + (-7)^2}$
Calculate Squares: We calculate $0^2$ and $(-7)^2$ . Since $0^2 = 0$ and $(-7)^2 = 49$ , we have: $\newline$ $|-7i| = \sqrt{0 + 49}$
Simplify Square Root: Simplify the expression inside the square root: $|-7i| = \sqrt{49}$
Final Absolute Value Calculation: The square root of $49$ is $7$ , so the absolute value of $|-7i|$ is: $\newline$ $|-7i| = 7$

More problems from Absolute values of complex numbers

Question

\newline

8i + 6i

\newline

\newline

Write your answer in the form

a + bi

Posted 5 months ago

Question

Find the complex conjugate of the given number.

\newline

4 + 10i

\newline

\newline

Write your answer in the form

a + bi

Posted 5 months ago

Question

\newline

\frac{{-4i}}{{-9i}}

\newline

\newline

Write your simplified answer in the form

a + bi

Posted 5 months ago

Question

Combine the like terms to create an equivalent expression.

\newline

7k-k+19=\boxed{\phantom{0}}

Posted 10 months ago

Question

Apply the distributive property to factor out the greatest common factor.

\newline

9+12 n=

Posted 5 months ago

Question

Solve the equation.

\newline

\begin{aligned} & 12=n-9 \\ n= & \square \end{aligned}

Posted 10 months ago

Question

What is the amplitude of

y=-\sin (8 x-3)+5

\newline

Posted 8 months ago

Question

What is the period of

\newline

y=4 \sin (-2 x+7)-1 \text { ? }

\newline

Give an exact value.

\newline

Posted 8 months ago

Question

3 \cdot(3+20 i)=

\newline

Your answer should be a complex number in the form

a+b i

a

b

are real numbers.

Posted 10 months ago

Question

(35-23 i)+(13+25 i)=

\newline

Express your answer in the form

(a+b i)

Posted 8 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant