en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ((1+i)^9)/((1-i)^7)

Solution

simplify

\frac{( 1 + i ) ^{9}}{( 1 - i ) ^{7}}

Solution

2

Solution steps

\frac{( 1 + i ) ^{9}}{( 1 - i ) ^{7}}

Expand

(1 - i)^{7} : 8 i + 8

= \frac{( 1 + i ) ^{9}}{8 i + 8}

Factor

8 i + 8 : 8 (i + 1)

= \frac{( 1 + i ) ^{9}}{8 ( i + 1 )}

Apply the commutative law:

1 + i = i + 1

= \frac{( i + 1 ) ^{9}}{8 ( i + 1 )}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(i + 1)^{9} = (i + 1) (i + 1)^{8}

= \frac{( i + 1 ) ( i + 1 ) ^{8}}{8 ( i + 1 )}

Cancel the common factor:

i + 1

= \frac{( i + 1 ) ^{8}}{8}

Simplify

\frac{( i + 1 ) ^{8}}{8} : 2

= 2

Popular Examples

expand (sec(θ)+tan(θ))(1-sin(θ))expand

(sec (θ) + tan (θ)) (1 - sin (θ))

expand (cos^2(x)-ycos(x))dx-(1+sin(x))dy expand

(cos^{2} (x) - y cos (x)) d x - (1 + sin (x)) d y

expand (6e-6r)(2e-9r)expand

(6 e - 6 r) (2 e - 9 r)

expand (sin(x)-1)^2 expand

(sin (x) - 1)^{2}

expand (e-1)^3 expand

(e - 1)^{3}

Frequently Asked Questions (FAQ)

What is ((1+i)^9)/((1-i)^7) ?
The solution to ((1+i)^9)/((1-i)^7) is 2