What is (7+3i)(7-3i)-(7-3i)^2-(7-3i)^3 ?

The solution to (7+3i)(7-3i)-(7-3i)^2-(7-3i)^3 is -136+456i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (7+3i)(7-3i)-(7-3i)^2-(7-3i)^3

simplify

(7 + 3 i) (7 - 3 i) - (7 - 3 i)^{2} - (7 - 3 i)^{3}

- 136 + 456 i

Solution steps

(7 + 3 i) (7 - 3 i) - (7 - 3 i)^{2} - (7 - 3 i)^{3}

(7 + 3 i) (7 - 3 i) = 7^{2} + 3^{2}

(7 - 3 i)^{2} = - 42 i + 40

(7 - 3 i)^{3} = - 414 i + 154

= 7^{2} + 3^{2} - (- 42 i + 40) - (- 414 i + 154)

Expand

- (- 42 i + 40) : 42 i - 40

= 7^{2} + 3^{2} + 42 i - 40 - (- 414 i + 154)

Expand

- (- 414 i + 154) : 414 i - 154

= 7^{2} + 3^{2} + 42 i - 40 + 414 i - 154

Group like terms

= 42 i + 414 i + 7^{2} + 3^{2} - 40 - 154

Add similar elements:

42 i + 414 i = 456 i

= 456 i + 7^{2} + 3^{2} - 40 - 154

Subtract the numbers:

- 40 - 154 = - 194

= 456 i + 7^{2} + 3^{2} - 194

7^{2} = 49

3^{2} = 9

= 456 i + 49 + 9 - 194

Add the numbers:

49 + 9 - 194 = - 136

= 456 i - 136

Rewrite in standard complex form:

- 136 + 456 i

= - 136 + 456 i

1^{50}

3^{7}

3^{4} \times 3^{3}

(- 4 x + 5) (3 x^{2} - 2 x - 1)

12 \frac{1}{2} - 2 \frac{1}{4} - 3 \frac{3}{8}

What is (7+3i)(7-3i)-(7-3i)^2-(7-3i)^3 ?
The solution to (7+3i)(7-3i)-(7-3i)^2-(7-3i)^3 is -136+456i