Question

Write standart form of complex number 5(cos135^@+isin135^@)

Complex numbers
ANSWERED
asked 2021-01-07
Write standart form of complex number \(\displaystyle{5}{\left({{\cos{{135}}}^{\circ}+}{i}{\sin{{135}}}^{\circ}\right)}\)

Answers (1)

2021-01-08
Standart form of complex number, \(\displaystyle{z}={r}{\left({\cos{\theta}}+{i}{\sin{\theta}}\right)}\), is z = a+ib
Calculate the values of cosine and sine,
\(\displaystyle{\cos{{\left({135}^{\circ}\right)}}}=-\frac{{1}}{\sqrt{{2}}}\)
\(\displaystyle{\sin{{\left({135}^{\circ}=\frac{{1}}{\sqrt{{2}}}\right.}}}\)
Substitute the values od cosine and sine in \(\displaystyle{z}={5}{\left({{\cos{{135}}}^{\circ}+}{i}{\sin{{135}}}^{\circ}\right)},\)
\(\displaystyle{z}={5}{\left({{\cos{{135}}}^{\circ}+}{i}{\sin{{135}}}^{\circ}\right)}={5}{\left(-\frac{{1}}{\sqrt{{2}}}+{i}\frac{{1}}{\sqrt{{2}}}\right)}=-\frac{{5}}{\sqrt{{2}}}+\frac{{t}}{\sqrt{{2}}}{i}\)
Rationalise the complex number, \(\displaystyle{z}=-\frac{{5}}{\sqrt{{2}}}+\frac{{t}}{\sqrt{{2}}}{i},{z}=-\frac{{{5}\sqrt{{2}}}}{{2}}+\frac{{{5}\sqrt{{2}}}}{{2}}{i}\)
0
 
Best answer

expert advice

Need a better answer?

Relevant Questions

asked 2021-01-24

Write each complex number in standard form. \(2(\cos 30^{\circ} + i \sin 30^{\circ})\)

 

asked 2021-02-15

Write the complex number in trigonometric form \(r(\cos \theta + i \sin \theta)\),with theta in the interval \(\displaystyle{\left[{0}^{\circ},{360}^{\circ}\right]}\)
\(\displaystyle{5}\sqrt{{3}}+{5}{i}\)

asked 2021-05-29
Complex number in rectangular form What is (1+2j) + (1+3j)? Your answer should contain three significant figures.
asked 2020-12-07
Write the complex number in standart form \(\displaystyle{6}{i}^{{2}}-{8}{i}^{{3}}\)
asked 2020-11-30
Write the standard form of the complex number.
\(\displaystyle{12}{\left({\cos{{\left({60}^{\circ}\right)}}}+{i}{\sin{{\left({60}^{\circ}\right)}}}\right)}\)
asked 2020-11-08
Adam starts with the number z=1+2i on the complex plane. First, he dilates z by factor of 2 about the origin. Then, he reflects it across the real axis. Finally, he rotates it \(\displaystyle{90}^{\circ}\) counterclockwise about the origin. The resulting complex number can be written in form a+bi where a and b are real numers. What is the resukring complex number?
asked 2021-05-09
State any restrictions on the variable in the complex fraction. \(\displaystyle{\frac{{{\frac{{{x}-{4}}}{{{x}+{4}}}}}}{{{\frac{{{x}^{{{2}}}-{1}}}{{{x}}}}}}}\)
asked 2020-12-17
Use DeMoivre’s Theorem to find the indicated power of the complex number .Write answer in rectangular form.
\(\displaystyle{\left(\sqrt{{3}}-{i}\right)}^{{6}}\)
asked 2020-11-01
Find the principal argument and exponential form of \(\displaystyle{z}=\frac{{i}}{{{1}+{i}}}\) If z=x+iy is a complex number
asked 2021-05-09

Write the complex number in standard form.
\(5+\sqrt{-36}\)

...