What is ((a+bi)+1)/(2(a+bi)-5) ?

The solution to ((a+bi)+1)/(2(a+bi)-5) is (-5+2a^2+2b^2-3a)/((-5+2a)^2+4b^2)-i(7b)/((-5+2a)^2+4b^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ((a+bi)+1)/(2(a+bi)-5)

simplify

\frac{( a + bi ) + 1}{2 ( a + bi ) - 5}

\frac{- 5 + 2 a ^{2} + 2 b ^{2} - 3 a}{( - 5 + 2 a ) ^{2} + 4 b ^{2}} - i \frac{7 b}{( - 5 + 2 a ) ^{2} + 4 b ^{2}}

Solution steps

\frac{( a + bi ) + 1}{2 ( a + bi ) - 5}

Remove parentheses:

(a) = a

= \frac{a + bi + 1}{2 ( a + bi ) - 5}

Rationalize

\frac{a + ib + 1}{2 ( a + ib ) - 5} : \frac{2 b ^{2} - 7 ib + ( a + 1 ) ( 2 a - 5 )}{4 b ^{2} + ( 2 a - 5 ) ^{2}}

= \frac{( a + 1 ) ( 2 a - 5 ) + 2 b ^{2} - 7 ib}{( 2 a - 5 ) ^{2} + 4 b ^{2}}

Rewrite

\frac{( a + 1 ) ( 2 a - 5 ) + 2 b ^{2} - 7 ib}{( 2 a - 5 ) ^{2} + 4 b ^{2}}

in standard complex form:

\frac{2 a ^{2} - 3 a - 5 + 2 b ^{2}}{4 b ^{2} + ( - 5 + 2 a ) ^{2}} - \frac{7 b}{4 b ^{2} + ( 2 a - 5 ) ^{2}} i

= \frac{2 a ^{2} - 3 a - 5 + 2 b ^{2}}{4 b ^{2} + ( - 5 + 2 a ) ^{2}} - \frac{7 b}{4 b ^{2} + ( 2 a - 5 ) ^{2}} i

- 30 a^{3} + 8 a^{2} + 8 a

e^{l n (e^{x})}

8 \div \frac{1}{7}

(2 r - 5)^{3}

\frac{11}{4} + \frac{27}{5}

What is ((a+bi)+1)/(2(a+bi)-5) ?
The solution to ((a+bi)+1)/(2(a+bi)-5) is (-5+2a^2+2b^2-3a)/((-5+2a)^2+4b^2)-i(7b)/((-5+2a)^2+4b^2)