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To multiply two complex numbers z1 = a + bi and z2 = c + di, use the formula: z1 * z2 = (ac - bd) + (ad + bc)i. What is a complex number? A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.
Jan 18, 2024 · Find the magnitude of z = 5 + 7i, to get |z| = √ (52+ 72) = 8.602. Compute the phase angle of z = 5 + 7i, to get ϕ = tan-1(7/5) = 0.951 rad. Use the complex natural log formula ln (z) = ln|z| + iϕ to get ln (5+7i) = ln|8.602| + i0.951 = 2.152 + 0.951i. You can verify your result with our imaginary number calculator.
Complex Number Calculator. Step 1: Enter the equation for which you want to find all complex solutions. The Complex Number Calculator solves complex equations and gives real and imaginary solutions. Step 2: Click the blue arrow to submit.
Jan 20, 2024 · When b = 0 b = 0 b = 0, the number is purely real, and if a = 0 a = 0 a = 0, we have a purely imaginary number. You can use this complex number calculator as an imaginary number calculator - just input the real component equal to 0.
This calculator does basic arithmetic on complex numbers and evaluates expressions in the set of complex numbers. As an imaginary unit, use i or j (in electrical engineering), which satisfies the basic equation i 2 = −1 or j 2 = −1. The calculator also converts a complex number into angle notation (phasor notation), exponential, or polar ...
May 17, 2024 · φ. \varphi φ: sin ( φ) \sin (\varphi) sin(φ). Multiply the result of the previous step by the magnitude. ∣ z ∣. |z| ∣z∣ of the complex number: the result is the imaginary part of our number: I m = ∣ z ∣ ⋅ sin ( φ) \mathrm {Im} = |z|\cdot\sin (\varphi) Im = ∣z∣ ⋅ sin(φ).
Discover the world of imaginary numbers with our Imaginary Number Calculator. Calculate, learn, and explore the wild side of numbers.
