1/z = 1/(9+16i) + 1/(20-10i)

Divide: 1 / 1 = 1

Complex number: 9+16i

Divide: the result of step No. 1 / the result of step No. 2 = 1 / (9+16i) = 1/

9+16i

= 1*(9-16i)/

(9+16i)*(9-16i)

= 1 * 9 + 1 * (-16i)/

9 * 9 + 9 * (-16i) + 16i * 9 + 16i * (-16i)

= 9-16i/

81-144i+144i-256i2

= 9-16i/

81-144i+144i+256

= 9 +i(-16)/

81 + 256 +i(-144 + 144)

= 9-16i/

337

= 0.0267062-0.0474777i

To divide complex numbers, you must multiply both (numerator and denominator) by the conjugate of the denominator. To find the conjugate of a complex number, you change the sign in imaginary part.

Distribute in both the numerator and denominator to remove the parenthesis and add and simplify. Use rule .

ei 0 = ei 0 : 18.3575598 × ei 1.0584069 = 18.3575598 × ei 0.3369014 π = (1 / 18.3575598) × ei (0-0.3369014) = 0.0544735 × ei -1.0584069 = 0.0544735 × ei (-0.3369014) π = 0.0267062-0.0474777i

Complex number: 20-10i

Divide: 1 / the result of step No. 4 = 1 / (20-10i) = 1/

20-10i

= 1*(20+10i)/

(20-10i)*(20+10i)

= 1 * 20 + 1 * 10i/

20 * 20 + 20 * 10i + (-10i) * 20 + (-10i) * 10i

= 20+10i/

400+200i-200i-100i2

= 20+10i/

400+200i-200i+100

= 20 +i(10)/

400 + 100 +i(200 - 200)

= 20+10i/

500

= 0.04+0.02i

To divide complex numbers, you must multiply both (numerator and denominator) by the conjugate of the denominator. To find the conjugate of a complex number, you change the sign in imaginary part.

Distribute in both the numerator and denominator to remove the parenthesis and add and simplify. Use rule .

ei 0 = ei 0 : 22.3606798 × ei -0.4636476 = 22.3606798 × ei (-0.1475836) π = (1 / 22.3606798) × ei (0-(-0.1475836)) = 0.0447214 × ei 0.4636476 = 0.0447214 × ei 0.1475836 π = 0.04+0.02i

Add: the result of step No. 3 + the result of step No. 5 = (0.0267062-0.0474777i) + (0.04+0.02i) = (0.0267062+0.04) + (-0.0474777+0.02)i = 0.0667062-0.0274777i

Step-by-step explanation: