# Write without absolute value notation: abs(6-5i)

Question
Piecewise-Defined Functions
Write without absolute value notation: $$\displaystyle{\left|{{6}-{5}{i}}\right|}$$

2021-02-14
Step 1
Absolute value of a complex number:
The absolute value of a complex number z=x+iy is given by $$\displaystyle{\left|{{z}}\right|}={\left|{{x}+{i}{y}}\right|}=\sqrt{{{x}^{{2}}+{y}^{{2}}}}$$.
The given complex number is 6-5i.
Step 2
Evaluate the value of $$\displaystyle{\left|{{6}−{5}{i}}\right|}$$ as follows.
$$\displaystyle{\left|{{6}-{5}{i}}\right|}=\sqrt{{{6}^{{2}}+{\left(-{5}\right)}^{{2}}}}$$
$$\displaystyle=\sqrt{{{36}+{25}}}$$
$$\displaystyle=\sqrt{{{61}}}$$
$$\displaystyle\approx{7.81}$$
Therefore, the absolute value of $$\displaystyle{\left|{{6}−{5}{i}}\right|}$$ is 7.81.

### Relevant Questions

Rewrite expression without absolute value bars.
$$\displaystyle{\left|{\sqrt{{5}}-{13}}\right|}$$
Rewrite the expression without using the absolute value symbol.
$$\displaystyle{\left|{{3}{x}-{5}}\right|}$$ if $$\displaystyle{x}\ge\frac{{5}}{{3}}$$
Rewrite expression without absolute value bars.
$$\displaystyle{\left|{{7}-\pi}\right|}$$
The absolute value gives us the "size" or magnitude of a number. Find each of the following.
a)$$\displaystyle{\left|{-{7}}\right|}$$
b)$$\displaystyle{\left|{-{2}}\right|}$$
c)$$\displaystyle{\left|{{6}}\right|}$$
d)$$\displaystyle{\left|{{0}}\right|}$$
Write each expression without using absolute value symbols.
$$|0|$$
Which of the following correctly uses absolute value to show the distance between -80 and 15?
A.
$$\displaystyle{\left|{-{80}-{15}}\right|}={\left|{-{95}}\right|}=-{95}$$ units
B.
$$\displaystyle{\left|{-{80}+{15}}\right|}={\left|{-{65}}\right|}={65}$$ units
C.
$$\displaystyle{\left|{-{80}-{15}}\right|}={\left|{-{95}}\right|}={95}$$ units
D.
$$\displaystyle{\left|{-{80}+{15}}\right|}={\left|{-{65}}\right|}=-{65}$$ units
Step 1
Solve absolute value inequality.
$$\displaystyle-{4}{\left|{{1}-{x}}\right|}{<}-{16}$$
a. $$\displaystyle{\left|{{7}}\right|}=$$?
b. $$\displaystyle{\left|{-{7}}\right|}=$$?
c. $$\displaystyle-{\left|{{7}}\right|}=$$?
d. $$\displaystyle-{\left|{-{7}}\right|}=$$?
Solve absolute value inequality : $$\displaystyle{\left|{{x}+{3}}\right|}\le{4}$$
The absolute value of $$\displaystyle-{\left|{-{45}}\right|}$$