What is (2+(3i)/n)^2 ?

The solution to (2+(3i)/n)^2 is (4n^2-9}{n^2}+\frac{12)/n i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (2+(3i)/n)^2

simplify

(2 + \frac{3 i}{n})^{2}

\frac{4 n ^{2} - 9}{n ^{2}} + \frac{12}{n} i

Solution steps

(2 + \frac{3 i}{n})^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(2 + \frac{3 i}{n})^{2} = 2^{2} + 2 \cdot 2 \cdot \frac{3 i}{n} + (\frac{3 i}{n})^{2}

= 2^{2} + 2 \cdot 2 \cdot \frac{3 i}{n} + (\frac{3 i}{n})^{2}

2^{2} = 4

2 \cdot 2 \cdot \frac{3 i}{n} = 4 \cdot \frac{3 i}{n}

(\frac{3 i}{n})^{2} = - \frac{9}{n ^{2}}

= 4 + 4 \cdot \frac{3 i}{n} - \frac{9}{n ^{2}}

Simplify

4 + 4 \cdot \frac{3 i}{n} - \frac{9}{n ^{2}} : \frac{4 n ^{2} - 9}{n ^{2}} + \frac{12}{n} i

= \frac{4 n ^{2} - 9}{n ^{2}} + \frac{12}{n} i

(x + 1 - 2)^{2}

(4 + 3 i)^{5}

\frac{( 6 x - 5 ) ^{2}}{36}

(\frac{1}{p ^{2}} - 4 q)^{7}

(x^{2} + 4 i)^{2}

What is (2+(3i)/n)^2 ?
The solution to (2+(3i)/n)^2 is (4n^2-9}{n^2}+\frac{12)/n i